Amber 10 Users' Manual - glycam [PDF]

Amber 10 Users’ Manual Principal contributors to the current codes: David A. Case (The Scripps Research Institute) Tom Darden (NIEHS) Thomas E. Cheatham III (Utah) Carlos Simmerling (Stony Brook) Junmei Wang (UT Southwestern Medical Center) Robert E. Duke (NIEHS and UNC-Chapel Hill) Ray Luo (UC Irvine) Mike Crowley (NREL) Ross Walker (SDSC) Wei Zhang (TSRI) Kenneth M. Merz (Florida) Bing Wang (Florida) Seth Hayik (Florida) Adrian Roitberg (Florida) Gustavo Seabra (Florida) István Kolossváry (Budapest and D.E. Shaw)

Kim F. Wong (University of Utah) Francesco Paesani (University of Utah) Jiri Vanicek (EPL-Lausanne) Xiongwu Wu (NIH) Scott R. Brozell (TSRI) Thomas Steinbrecher (TSRI) Holger Gohlke (Kiel) Lijiang Yang (UC Irvine) Chunhu Tan (UC Irvine) John Mongan (UC San Diego) Viktor Hornak (Stony Brook) Guanglei Cui (Stony Brook) David H. Mathews (Rochester) Matthew G. Seetin (Rochester) Celeste Sagui (North Carolina State) Volodymyr Babin (North Carolina State) Peter A. Kollman (UC San Francisco)

Additional key contributors to earlier versions: David A. Pearlman (UC San Francisco) Robert V. Stanton (UC San Francisco) Jed Pitera (UC San Francisco) Irina Massova (UC San Francisco) Ailan Cheng (Penn State) James J. Vincent (Penn State) Paul Beroza (Telik)

Vickie Tsui (TSRI) Christian Schafmeister (Pitt) Wilson S. Ross (UC San Francisco) Randall Radmer (UC San Francisco) George L. Seibel (UC San Francisco) James W. Caldwell (UC San Francisco) U. Chandra Singh (UC San Francisco) Paul Weiner (UC San Francisco)

Additional key people involved in force field development: Piotr Cieplak (Burnham Institute) Yong Duan (U.C. Davis) Rob Woods (Georgia) Karl Kirschner (Georgia) Sarah M. Tschampel (Georgia)

Alexey Onufriev (Virginia Tech.) Christopher Bayly (Merck-Frost) Wendy Cornell (UC San Francisco) Scott Weiner (UC San Francisco) Austin Yongye (Georgia) Matthew Tessier (Georgia)

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Acknowledgments Research support from DARPA, NIH and NSF for Peter Kollman is gratefully acknowledged, as is support from NIH, NSF, ONR and DOE for David Case. Use of the facilities of the UCSF Computer Graphics Laboratory (Thomas Ferrin, PI) is appreciated. The pseudocontact shift code was provided by Ivano Bertini of the University of Florence. We thank Chris Bayly and Merck-Frosst, Canada for permission to include charge increments for the AM1-BCC charge scheme. Many people helped add features to various codes; these contributions are described in the documentation for the individual programs; see also http://amber.scripps.edu/contributors.html. Recommended Citations: When citing Amber Version 10 in the literature, the following citation should be used: D.A. Case, T.A. Darden, T.E. Cheatham, III, C.L. Simmerling, J. Wang, R.E. Duke, R. Luo, M. Crowley, R.C. Walker, W. Zhang, K.M. Merz, B. Wang, S. Hayik, A. Roitberg, G. Seabra, I. Kolossváry, K.F. Wong, F. Paesani, J. Vanicek, X. Wu, S.R. Brozell, T. Steinbrecher, H. Gohlke, L. Yang, C. Tan, J. Mongan, V. Hornak, G. Cui, D.H. Mathews, M.G. Seetin, C. Sagui, V. Babin, and P.A. Kollman (2008), AMBER 10, University of California, San Francisco. The history of the codes and a basic description of the methods can be found in two papers: • D.A. Pearlman, D.A. Case, J.W. Caldwell, W.S. Ross, T.E. Cheatham, III, S. DeBolt, D. Ferguson, G. Seibel, and P. Kollman. AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules. Comp. Phys. Commun. 91, 1-41 (1995). • D.A. Case, T. Cheatham, T. Darden, H. Gohlke, R. Luo, K.M. Merz, Jr., A. Onufriev, C. Simmerling, B. Wang and R. Woods. The Amber biomolecular simulation programs. J. Computat. Chem. 26, 1668-1688 (2005). Peter Kollman died unexpectedly in May, 2001. We dedicate Amber to his memory. Cover Illustration The cover shows E. coli KAS I (FabB) fatty acid synthase (pdb code 1fj4), a drug target of particular interest for the development of novel antibiotics. Overlaying the enzyme the chemical formula of a naturally occurring inhibitor, thiolactomycin, is drawn with six "computational alchemy" ligand transformations recently studied by free energy calculations. [1, 2] The picture was prepared by Thomas Steinbrecher using VMD, povray 3.6 and ChemDraw.

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Contents Contents

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1. Introduction

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1.1. What to read next . . . . . . . . . . . . . . . . . . . . . . 1.2. Information flow in Amber . . . . . . . . . . . . . . . . . 1.2.1. Preparatory programs . . . . . . . . . . . . . . . . 1.2.2. Simulation programs . . . . . . . . . . . . . . . . 1.2.3. Analysis programs . . . . . . . . . . . . . . . . . 1.3. Installation of Amber 10 . . . . . . . . . . . . . . . . . . 1.3.1. More information on parallel machines or clusters 1.3.2. Installing Non-Standard Features . . . . . . . . . 1.3.3. Installing on Microsoft Windows . . . . . . . . . . 1.3.4. Testing . . . . . . . . . . . . . . . . . . . . . . . 1.3.5. Memory Requirements . . . . . . . . . . . . . . . 1.4. Basic tutorials . . . . . . . . . . . . . . . . . . . . . . . .

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2. Sander basics

2.1. 2.2. 2.3. 2.4. 2.5. 2.6.

Introduction . . . . . . . . . . . . . . . . . . . Credits . . . . . . . . . . . . . . . . . . . . . . File usage . . . . . . . . . . . . . . . . . . . . Example input files . . . . . . . . . . . . . . . Overview of the information in the input file . . General minimization and dynamics parameters 2.6.1. General flags describing the calculation 2.6.2. Nature and format of the input . . . . . 2.6.3. Nature and format of the output . . . . 2.6.4. Frozen or restrained atoms . . . . . . . 2.6.5. Energy minimization . . . . . . . . . . 2.6.6. Molecular dynamics . . . . . . . . . . 2.6.7. Self-Guided Langevin dynamics . . . . 2.6.8. Temperature regulation . . . . . . . . . 2.6.9. Pressure regulation . . . . . . . . . . . 2.6.10. SHAKE bond length constraints . . . . 2.6.11. Water cap . . . . . . . . . . . . . . . . 2.6.12. NMR refinement options . . . . . . . . 2.7. Potential function parameters . . . . . . . . . . 2.7.1. Generic parameters . . . . . . . . . . . 2.7.2. Particle Mesh Ewald . . . . . . . . . .

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19 21 21 22 23 23 23 24 25 27 27 28 28 29 31 32 33 34 34 35 36

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CONTENTS 2.7.3. Using IPS for the calculation of nonbonded interactions 2.7.4. Extra point options . . . . . . . . . . . . . . . . . . . . 2.7.5. Polarizable potentials . . . . . . . . . . . . . . . . . . . 2.7.6. Dipole Printing . . . . . . . . . . . . . . . . . . . . . . 2.7.7. Detailed MPI Timings . . . . . . . . . . . . . . . . . . 2.8. Varying conditions . . . . . . . . . . . . . . . . . . . . . . . . 2.9. File redirection commands . . . . . . . . . . . . . . . . . . . . 2.10. Getting debugging information . . . . . . . . . . . . . . . . . .

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3.1. The Generalized Born/Surface Area Model . . . . . . . . . . . . 3.1.1. GB/SA input parameters . . . . . . . . . . . . . . . . . . 3.1.2. ALPB (Analytical Linearized Poisson-Boltzmann) . . . . 3.2. Poisson-Boltzmann calculations . . . . . . . . . . . . . . . . . . 3.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Usage and keywords . . . . . . . . . . . . . . . . . . . . 3.2.3. Example inputs . . . . . . . . . . . . . . . . . . . . . . . 3.3. Empirical Valence Bond . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. General usage description . . . . . . . . . . . . . . . . . 3.3.3. Biased sampling . . . . . . . . . . . . . . . . . . . . . . 3.3.4. Quantization of nuclear degrees of freedom . . . . . . . . 3.3.5. Distributed Gaussian EVB . . . . . . . . . . . . . . . . . 3.3.6. EVB input variables and interdependencies . . . . . . . . 3.4. Using the AMOEBA force field . . . . . . . . . . . . . . . . . . 3.5. QM/MM calculations . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1. The hybrid QM/MM potential . . . . . . . . . . . . . . . 3.5.2. The QM/MM interface and link atoms . . . . . . . . . . . 3.5.3. Generalized Born implicit solvent . . . . . . . . . . . . . 3.5.4. Ewald and PME . . . . . . . . . . . . . . . . . . . . . . 3.5.5. Hints for running successful QM/MM calculations . . . . 3.5.6. General QM/MM &qmmm Namelist Variables . . . . . . 3.5.7. Link Atom Specific QM/MM &qmmm Namelist Variables

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4.1. Thermodynamic integration . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Basic inputs for thermodynamic integration . . . . . . . . . 4.1.2. Softcore Potentials in Thermodynamic Integration . . . . . 4.2. Umbrella sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Targeted MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Steered Molecular Dynamics (SMD) and the Jarzynski Relationship 4.4.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Implementation and usage . . . . . . . . . . . . . . . . . . 4.5. Replica Exchange Molecular Dynamics (REMD) . . . . . . . . . . 4.5.1. Changes to REMD in Amber 10 . . . . . . . . . . . . . . . 4.5.2. Running REMD simulations . . . . . . . . . . . . . . . . .

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3. Force field modifications

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4. Sampling and free energies

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38 39 39 40 41 41 46 46 51 53 56 57 57 60 66 69 69 70 73 75 76 78 84 86 87 88 89 89 90 91 97 99

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4.9.

4.5.3. Restarting REMD simulations . . . . . . . . . . . . . . . . . . 4.5.4. Content of the output files . . . . . . . . . . . . . . . . . . . . 4.5.5. Major changes from sander when using replica exchange . . . . 4.5.6. Cautions when using replica exchange . . . . . . . . . . . . . . 4.5.7. Replica exchange example . . . . . . . . . . . . . . . . . . . . 4.5.8. Replica exchange using a hybrid solvent model . . . . . . . . . 4.5.9. Changes to hybrid REMD in Amber 10 . . . . . . . . . . . . . 4.5.10. Cautions for hybrid solvent replica exchange . . . . . . . . . . 4.5.11. Reservoir REMD . . . . . . . . . . . . . . . . . . . . . . . . . Adaptively biased MD, steered MD, and umbrella sampling with REMD 4.6.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2. Reaction Coordinates . . . . . . . . . . . . . . . . . . . . . . . 4.6.3. Steered Molecular Dynamics . . . . . . . . . . . . . . . . . . . 4.6.4. Umbrella sampling . . . . . . . . . . . . . . . . . . . . . . . . 4.6.5. Adaptively Biased Molecular Dynamics . . . . . . . . . . . . . Nudged elastic band calculations . . . . . . . . . . . . . . . . . . . . . 4.7.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2. Preparing input files for NEB . . . . . . . . . . . . . . . . . . 4.7.3. Input Variables . . . . . . . . . . . . . . . . . . . . . . . . . . Constant pH calculations . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2. Preparing a system for constant pH . . . . . . . . . . . . . . . 4.8.3. Running at constant pH . . . . . . . . . . . . . . . . . . . . . . 4.8.4. Analyzing constant pH simulations . . . . . . . . . . . . . . . 4.8.5. Extending constant pH to additional titratable groups . . . . . . Low-MODe (LMOD) methods . . . . . . . . . . . . . . . . . . . . . . 4.9.1. LMOD conformational searching and flexible docking . . . . . 4.9.2. LMOD Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.3. XMIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.4. LMOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9.5. Tricks of the trade of running LMOD searches . . . . . . . . .

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5. Quantum dynamics

5.1. Path-Integral Molecular Dynamics . . . . . . . . . . 5.1.1. General theory . . . . . . . . . . . . . . . . 5.1.2. How PIMD works in Amber . . . . . . . . . 5.2. Centroid Molecular Dynamics (CMD) . . . . . . . . 5.2.1. Implementation and input/output files . . . . 5.2.2. Examples . . . . . . . . . . . . . . . . . . . 5.3. Ring Polymer Molecular Dynamics (RPMD) . . . . 5.3.1. Input parameters . . . . . . . . . . . . . . . 5.3.2. Examples . . . . . . . . . . . . . . . . . . . 5.4. Reactive Dynamics . . . . . . . . . . . . . . . . . . 5.4.1. Path integral quantum transition state theory . 5.4.2. Quantum Instanton . . . . . . . . . . . . . . 5.5. Isotope effects . . . . . . . . . . . . . . . . . . . . .

113 113 114 115 115 117 118 118 119 121 121 122 125 126 127 130 130 132 133 133 133 134 135 136 137 139 139 140 141 142 145 147

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147 147 149 153 154 155 156 156 156 156 156 157 160

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CONTENTS 5.5.1. 5.5.2. 5.5.3. 5.5.4. 5.5.5.

Thermodynamic integration with respect to mass . . . . . . AMBER implementation . . . . . . . . . . . . . . . . . . . Equilibrium isotope effects . . . . . . . . . . . . . . . . . . Kinetic isotope effects . . . . . . . . . . . . . . . . . . . . Estimating the kinetic isotope effect using EVB/LES-PIMD

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6. NMR and X-ray refinement using SANDER

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6.1. Distance, angle and torsional restraints . . . . . . . . . . . . . . 6.1.1. Variables in the &rst namelist: . . . . . . . . . . . . . . 6.2. NOESY volume restraints . . . . . . . . . . . . . . . . . . . . 6.3. Chemical shift restraints . . . . . . . . . . . . . . . . . . . . . 6.4. Pseudocontact shift restraints . . . . . . . . . . . . . . . . . . . 6.5. Direct dipolar coupling restraints . . . . . . . . . . . . . . . . . 6.6. Residual CSA or pseudo-CSA restraints . . . . . . . . . . . . . 6.7. Preparing restraint files for Sander . . . . . . . . . . . . . . . . 6.7.1. Preparing distance restraints: makeDIST_RST . . . . . 6.7.2. Preparing torsion angle restraints: makeANG_RST . . . 6.7.3. Chirality restraints: makeCHIR_RST . . . . . . . . . . 6.7.4. Direct dipolar coupling restraints: makeDIP_RST . . . . 6.8. Getting summaries of NMR violations . . . . . . . . . . . . . . 6.9. Time-averaged restraints . . . . . . . . . . . . . . . . . . . . . 6.10. Multiple copies refinement using LES . . . . . . . . . . . . . . 6.11. Some sample input files . . . . . . . . . . . . . . . . . . . . . . 6.11.1. 1. Simulated annealing NMR refinement . . . . . . . . 6.11.2. Part of the RST.f file referred to above . . . . . . . . . 6.11.3. 3. Sample NOESY intensity input file . . . . . . . . . . 6.11.4. Residual dipolar restraints, prepared by makeDIP_RST: 6.11.5. A more complicated constraint . . . . . . . . . . . . . 6.12. X-ray Crystallography Refinement using SANDER . . . . . . .

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7. PMEMD

7.1. 7.2. 7.3. 7.4. 7.5. 7.6. 7.7.

Introduction . . . . . . . . . . . . . . Functionality . . . . . . . . . . . . . PMEMD-specific namelist variables . Slightly changed functionality . . . . Parallel performance tuning and hints Installation . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . .

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8.1. General instructions . . . . . . . . . . . . 8.2. Input explanations . . . . . . . . . . . . . 8.2.1. General . . . . . . . . . . . . . . 8.2.2. Energy Decomposition Parameters 8.2.3. Poisson-Boltzmann Parameters . 8.2.4. Molecular Mechanics Parameters

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8. MM_PBSA

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CONTENTS 8.2.5. Generalized Born Parameters . . . 8.2.6. Molsurf Parameters . . . . . . . . . 8.2.7. NMODE Parameters . . . . . . . . 8.2.8. Parameters for Snapshot Generation 8.2.9. Parameters for Alanine Scanning . 8.2.10. Trajectory Specification . . . . . . 8.3. Preparing the input file . . . . . . . . . . . 8.4. Auxiliary programs used by MM_PBSA . . 8.5. APBS as an alternate PB solver in Sander .

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9. LES

9.1. 9.2. 9.3. 9.4. 9.5. 9.6.

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Preparing to use LES with AMBER . . . . . . . . . . . . . . . . . . . . . . . Using the ADDLES program . . . . . . . . . . . . . . . . . . . . . . . . . . . More information on the ADDLES commands and options . . . . . . . . . . . Using the new topology/coordinate files with SANDER . . . . . . . . . . . . . Using LES with the Generalized Born solvation model . . . . . . . . . . . . . Case studies: Examples of application of LES . . . . . . . . . . . . . . . . . . 9.6.1. Enhanced sampling for individual functional groups: Glucose . . . . . 9.6.2. Enhanced sampling for a small region: Application of LES to a nucleic acid loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.3. Improving conformational sampling in a small peptide . . . . . . . . .

10. Divcon

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11. Miscellaneous

ambpdb . . . . protonate . . . ambmask . . . pol_h and gwh

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10.1. Introduction . . . . . . . . . . . . . 10.2. Getting Started . . . . . . . . . . . 10.2.1. Standard Jobs . . . . . . . . 10.2.2. Divide and Conquer Jobs . . 10.3. Keywords . . . . . . . . . . . . . . 10.3.1. Hamiltonians . . . . . . . . 10.3.2. Convergence Criterion . . . 10.3.3. Restrained Atoms . . . . . . 10.3.4. Output . . . . . . . . . . . 10.3.5. General . . . . . . . . . . . 10.3.6. Gradient . . . . . . . . . . . 10.3.7. Atomic Charges . . . . . . 10.3.8. Subsetting . . . . . . . . . . 10.4. Solvation . . . . . . . . . . . . . . 10.5. Nuclear Magnetic Resonance(NMR) 10.5.1. Default Keywords . . . . . 10.6. Citation Information . . . . . . . . 11.1. 11.2. 11.3. 11.4.

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7

CONTENTS 11.5. fantasian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 11.6. elsize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 A. Namelist Input Syntax

261

B. GROUP Specification

263

C. EVB output file specifications

267

D. Distributed Gaussian EVB format specifications

271

D.1. Cartesian coordinate representation . . . . . . . . . . . . . . . . . . . . . . . . 271 D.2. Internal coordinate representation . . . . . . . . . . . . . . . . . . . . . . . . 273

E. AMBER Trajectory NetCDF Format

E.1. E.2. E.3. E.4. E.5. E.6.

Introduction . . . . . . . . . Program behavior . . . . . . NetCDF file encoding . . . . Global attributes . . . . . . . Dimensions . . . . . . . . . Variables . . . . . . . . . . E.6.1. Label variables . . . E.6.2. forcedump.dat" This produces an ascii file. Default is zero. Set to one to dump forces.

rmsfrc

Flag to compare energies forces and virials as well as components of forces (bond, angle forces etc.) to those in the file "forcedump.dat". Default is zero. Set to one to compare forces.

Several other options are also possible to modify the calculated forces. zerochg

Flag to zero all charges before calculating forces. Default zero. Set to one to remove charges.

zerovdw

Flag to remove all van der Waals interactions before calculating forces. Default zero. Set to one to remove van der Waals.

zerodip

Flag to remove all atomic dipoles before calculating forces. Only relevant when polarizability is invoked.

do_dir, do_rec, do_adj, do_self, do_bond, do_cbond, do_angle, do_ephi, do_xconst, do_cap These are flags which turn on or off the subroutines they refer to. The defaults are one. Set to zero to prevent a subroutine from running. For example, set do_dir=0 to turn off the direct sum interactions (van der Waals as well as electrostatic). Thes options, as well as the zerochg, zerovdw,zerodip flags, can be used to fine tune a test of forces, accuracy etc. EXAMPLES: This input list tests the reciprocal sum forces on atom 14 numerically, using a delta of 10 -4.

47

2. Sander basics &debugf neglgdel=4, nranatm = 0, atomn = 14, do_debugf = 1,do_dir = 0,do_adj = 0,do_rec = 1, do_self = 0, do_bond = 1,do_angle = 0,do_ephi = 0, zerovdw = 0, zerochg = 0, chkvir = 0, dumpfrc = 0, rmsfrc = 0, /

This input list causes a dump of force components to "forcedump.dat". The bond, angle and dihedral forces are not calculated, and van der Waals interactions are removed, so the total force is the Ewald electrostatic force, and the only non-zero force components calculated are electrostatic. &debugf neglgdel=4, nranatm = 0, atomn = 0, do_debugf = 1,do_dir = 1,do_adj = 1,do_rec = 1, do_self = 1, do_bond = 0,do_angle = 0,do_ephi = 0, zerovdw = 1, zerochg = 0, chkvir = 0, dumpfrc = 1, rmsfrc = 0, /

In this case the same force components as above are calculated, and compared to those in "forcedump.dat". Typically this is used to get an RMS force error for the Ewald method in use. To do this, when doing the force dump use ewald or pme parameters to get high accuracy, and then normal parameters for the force compare: &debugf neglgdel=4, nranatm = 0, atomn = 0, do_debugf = 1,do_dir = 1,do_adj = 1,do_rec = 1, do_self = 1, do_bond = 0,do_angle = 0,do_ephi = 0, zerovdw = 1, zerochg = 0, chkvir = 0, dumpfrc = 0, rmsfrc = 1, /

For example, if you have a 40x40x40 unit cell and want to see the error for default pme options (cubic spline, 40x40x40 grid), run 2 jobs—— (assume box params on last line of inpcrd file) Sample input for 1st job: &cntrl dielc =1.0, scee = 1.2, cut = 11.0, nsnb = 5, ibelly = 0, ntx = 7, irest = 1, ntf = 2, ntc = 2, tol = 0.0000005, ntb = 1, ntp = 0, temp0 = 300.0, tautp = 1.0, nstlim = 1, dt = 0.002, maxcyc = 5, imin = 0, ntmin = 2,

48

2.10. Getting debugging information ntpr = 1, ntwx = 0, ntt = 0, ntr = 0, jfastw = 0, nmrmax=0, ntave = 25, / &debugf do_debugf = 1,do_dir = 1,do_adj = 1,do_rec = 1, do_self = 1, do_bond = 0,do_angle = 0,do_ephi = 0, zerovdw = 1, zerochg = 0, chkvir = 0, dumpfrc = 1, rmsfrc = 0, / &ewald nfft1=60,nfft2=60,nfft3=60,order=6, ew_coeff=0.35, /

Sample input for 2nd job: &cntrl dielc =1.0, scee = 1.2, cut = 8.0, nsnb = 5, ibelly = 0, ntx = 7, irest = 1, ntf = 2, ntc = 2, tol = 0.0000005, ntb = 1, ntp = 0, temp0 = 300.0, tautp = 1.0, nstlim = 1, dt = 0.002, maxcyc = 5, imin = 0, ntmin = 2, ntpr = 1, ntwx = 0, ntt = 0, ntr = 0, jfastw = 0, nmrmax=0, ntave = 25, / &debugf do_debugf = 1,do_dir = 1,do_adj = 1,do_rec = 1, do_self = 1, do_bond = 0,do_angle = 0,do_ephi = 0, zerovdw = 1, zerochg = 0, chkvir = 0, dumpfrc = 0, rmsfrc = 1, / &ewald ew_coeff=0.35, /

Note that an Ewald coefficient of 0.35 is close to the default error for an 8 Angstrom cutoff. However, the first job used an 11 Angstrom cutoff. The direct sum forces calculated in the 2nd job are compared to these, giving the RMS error due to an 8 Angstrom cutoff, with this value of ew_coeff. The reciprocal sum error calculated in the 2nd job is with respect to the pme reciprocal forces in the 1st job considered as "exact". Note further that if in these two jobs you had not specified "ew_coeff" sander would have calculated ew_coeff according to the cutoff and the direct sum tolerance, defaulted to 10−5 . This would give two different ewald coefficients. Under these circumstances the direct, reciprocal and adjust energies and forces would not agree well between the two jobs. However the total

49

2. Sander basics energy and forces should agree reasonably, (forces to within about 5x10−4 relative RMS force error) Since the totals are invariant to the coefficient. Finally, note that if other force components are calculated, such as van der Waals, bond, angle etc. The total force will include these, and the relative RMS force errors will be with respect to this total force in the denominator.

50

3. Force field modifications This chapter provides a number of sections describing how to use sander for particular types of problems. It should be read in conjunction with the previous chapter.

3.1. The Generalized Born/Surface Area Model The generalized Born solvation model can be used instead of explicit water for non-polarizable force fields such as ff94 or ff99. To estimate the total solvation free energy of a molecule, ∆Gsolv , one typically assumes that it can be decomposed into the "electrostatic" and "nonelectrostatic" parts: ∆Gsolv = ∆Gel + ∆Gnonel

(3.1)

where ∆Gnonel is the free energy of solvating a molecule from which all charges have been removed (i.e. partial charges of every atom are set to zero), and ∆Gel is the free energy of first removing all charges in the vacuum, and then adding them back in the presence of a continuum solvent environment. Generally speaking, ∆Gnonel comes from the combined effect of two types of interaction: the favorable van der Waals attraction between the solute and solvent molecules, and the unfavorable cost of breaking the structure of the solvent (water) around the solute. In the current Amber codes, this is taken to be proportional to the total solvent accessible surface area (SA) of the molecule, with a proportionality constant derived from experimental solvation energies of small non-polar molecules, and uses a fast LCPO algorithm [41] to compute an analytical approximation to the solvent accessible area of the molecule. The Poisson-Boltzmann approach described in the next section has traditionally been used in calculating ∆Gel . However, in molecular dynamics applications, the associated computational costs are often very high, as the Poisson-Boltzmann equation needs to be solved every time the conformation of the molecule changes. Amber developers have pursued an alternative approach, the analytic generalized Born (GB) method, to obtain a reasonable, computationally efficient estimate to be used in molecular dynamics simulations. The methodology has become popular, [42–49] especially in molecular dynamics applications, [50–53] due to its relative simplicity and computational efficiency, compared to the more standard numerical solution of the PoissonBoltzmann equation. Within Amber GB models, each atom in a molecule is represented as a sphere of radius Ri with a charge qi at its center; the interior of the atom is assumed to be filled uniformly with a material of dielectric constant 1. The molecule is surrounded by a solvent of a high dielectric ε (80 for water at 300 K). The GB model approximates ∆Gel by an analytical formula, [42, 54] ! " qi q j 1 exp[−κ fGB ] ∆Gel = − ∑ 1− 2 i j fGB (ri j , Ri , R j ) ε

(3.2)

51

3. Force field modifications where ri j is the distance between atoms i and j , the Ri are the so-called effective Born radii, and fGB () is a certain smooth function of its arguments. The electrostatic screening effects of (monovalent) salt are incorporated [54] via the Debye-Huckel screening parameter κ. A common choice [42] of fGB is # $1/2 fGB = ri2j + Ri R j exp(−ri2j /4Ri R j )

(3.3)

although other expressions have been tried. [45, 55] The effective Born radius of an atom reflects the degree of its burial inside the molecule: for an isolated ion, it is equal to its van der Waals (VDW) radius ρi . Then one obtains the particularly simple form: ∆Gel = −

q2i 2ρi

!

1−

1 ε

"

(3.4)

where we assumed κ = 0 (pure water). This is the famous expression due to Born for the solvation energy of a single ion. The function fGB () is designed to interpolate, in a clever manner, between the limit ri j → 0, when atomic spheres merge into one, and the opposite extreme ri j → ∞, when the ions can be treated as point charges obeying the Coulomb’s law. [48] For deeply buried atoms, the effective radii are large, Ri ( ρi , and for such atoms one can use a rough estimate Ri ≈ Li , where Li is the distance from the atom to the molecular surface. Closer to the surface, the effective radii become smaller, and for a completely solvent exposed side-chain one can expect Ri to approach ρi . The effective radii depend on the molecule’s conformation, and so have to be re-computed every time the conformation changes. This makes the computational efficiency a critical issue, and various approximations are normally made that facilitate an effective estimate of Ri . In particular, the so-called Coulomb field approximation, or CFA, is often used, which replaces the true electric displacement around the atom by the Coulomb field. Within this assumption, the following expression can be derived: [48] −1 R−1 i = ρi −

1 4π

%

θ (|r| − ρi )r−4 dr

(3.5)

where the integral is over the solute volume surrounding atom i. For a realistic molecule, the solute boundary (molecular surface) is anything but trivial, and so further approximations are made to obtain a closed-form analytical expression for the above equation, e.g. the so-called pairwise de-screening approach of Hawkins, Cramer and Truhlar, [56] which leads to a GB model implemented in Amber with igb=1. The 3D integral used in the estimation of the effective radii is performed over the van der Waals (VDW) spheres of solute atoms, which implies a definition of the solute volume in terms of a set of spheres, rather than the complex molecular surface, [57] commonly used in the PB calculations. For macromolecules, this approach tends to underestimate the effective radii for buried atoms, [48] arguably because the standard integration procedure treats the small vacuum–filled crevices between the van der Waals (VDW) spheres of protein atoms as being filled with water, even for structures with large interior. [55] This error is expected to be greatest for deeply buried atoms characterized by large effective radii, while for the surface atoms it is largely canceled by the opposing error arising from the Coulomb approximation, which tends [43, 47, 58] to overestimate Ri . The deficiency of the model described above can, to some extent, be corrected by noticing that even the optimal packing of hard spheres, which is a reasonable assumption for biomolecules,

52

3.1. The Generalized Born/Surface Area Model still occupies only about three quarters of the space, and so "scaling-up" of the integral by a factor of four thirds should effectively increase the underestimated radii by about the right amount, without any loss of computational efficiency. This idea was developed and applied in the context of pH titration, [48] where it was shown to improve the performance of the GB approximation in calculating pKa values of protein sidechains. However, the one-parameter correction introduced in Ref. [48] was not optimal in keeping the model’s established performance on small molecules. It was therefore proposed [53] to re-scale the effective radii with the re-scaling parameters being proportional to the degree of the atom’s burial, as quantified by the value Ii of the 3D integral. The latter is large for the deeply buried atoms and small for exposed ones. Consequently, one seeks a well-behaved re-scaling function, such that Ri ≈ (ρi−1 − Ii )−1 for small Ii , and Ri > (ρi−1 − Ii )−1 when Ii becomes large. The following simple, infinitely differentiable re-scaling function was chosen to replace the model’s original expression for the effective radii: ˜ i−1 − ρi−1 tanh(αΨ − β Ψ2 + γΨ3 ) R−1 i =ρ

(3.6)

where Ψ = Ii ρ˜ i , and α, β , γ are treated as adjustable dimensionless parameters which were optimized using the guidelines mentioned earlier (primarily agreement with the PB). Currently, Amber supports two GB models ( termed OBC ) based on this idea. These differ by the values of α, β , γ, and are invoked by setting igb to either igb=2 or igb=5. The details of the optimization procedure and the performance of the OBC model relative to the PB treatment and in MD simulations on proteins is described in Ref. [53]; an independent comparison to the PB in calculating the electrostatic part of solvation free energy on a large prmtop" and/or "inpcrd" exist in the current directory, which will be taken as topology and coordinate files correspondingly. If no command line options are given, the program prints the usage statement. The option -prnlev specifies how much (debugging) information is printed to stdout. If it is 0, only selected atoms are printed. More verbose output (which might be useful for debugging purposes) is achieved with higher values: 1 prints original "maskstr" in its tokenized (with operands enclosed in square brackets) and postfix (or Reverse Polish Notation) forms; number of atoms and residues in the topology file and number of selected atoms are also printed to stdout. 2 prints the resulting mask array, which is an array of integer values, with ’1’ representing a selected atom, and ’0’ an unselected one. Value of 3, in addition, prints mask arrays as they are pushed or popped from the stack (this is really only useful for tracing the problems occurring during stack operations). The -prnlev values of 0 or 1 should suffice for most uses. The option -out specifies the format of printed atoms. "short" means a condensed output using residue (:) and atom (@) designators followed by residue ranges and atom names. "pdb" (default) prints atoms in amber-like pdb format with the original "maskstr" printed as a REMARK at the top of the pdb file, and "amber" prints atom/residue ranges in the format suitable for copying into group input section of amber input file. The option -find is followed by "maskstr" expression. This is a string where some characters have a special meaning and thus express what parts (atoms/residues) of the molecule will get selected. The syntax of this string is explained in the section above (DESCRIPTION). If this option is left out, it defaults to ":*", which selects all atoms in the given topology file. The length of "maskstr" is limited to 80 characters. If the "maskstr" contains spaces or special characters (which would be expanded by the shell), it should be protected by single or double quotes (depending on the shell). In addition, for C-shells even a quoted exclamation character may be expanded for history substitution. Thus, it is recommended that the operand of the negation operator always be enclosed in parentheses so that "!" is always followed by a "(" to produce "!(" which disables the special history interpretation. For example, [@C= & !(@CA,C)] selects all carbons except backbone alpha and carbonyl carbon; the parentheses are redundant but shell safe. Another approach is to precede "!" with " man page indicates further ways to disable history substitution. FILES Assumes that prmtop and inpcrd files exists in the current directory if they are not specified with -p and -c options. Resulting (i.e. selected) atoms are written to stdout.

256

11.4. pol_h and gwh BUGS

Because all atom names are left justified in amber topology and the selections are case insensitive, there is no way to distinguish some atom names: alpha carbon CA and a calcium ion Ca are a notorious example of that.

11.4. pol_h and gwh NAME pol_h - set positions of polar hydrogens in proteins gwh - set positions of polar hydrogens onto water oxygen positions

SYNOPSIS pol_h < input-pqr-file > output-pdb-file gwh [-p ] [-w ] [-c] [-e] < input_pdb_file > output_pdb_file DESCRIPTION

The program pol_h resets positions of polar hydrogens of protein residues (Lys, Ser, Tyr and Thr), by optimizing simple electrostatic interactions. The input pqr file can be created by ambpdb. The program gwh sets positions of water hydrogens onto water oxygen positions that may be present in PDB files, by optimizing simple electrostatic interactions. If the -w flag is set, the program reads water oxygen positions from the file water-position-file, rather than the default name watpdb. If −c is set, a constant dielectric will be used to construct potentials, otherwise the (default) distant-dependent dielectric will be used. If −e is set, the electrostatic potential will be used to determine which hydrogens are placed first; otherwise, a distance criterion will be used. Accuracy of pol_h & gwh: * In the following the results for BPTI and RSA(ribonuclease A) are given together with those of Karplus(1) and Ornstein(2) groups. In the case of Ornstein’s method, it handles only some of hydrogens in question and therefore I normalized(scaled) their results using expected values for random generation. The rms deviation from the experimental positions (neutron diffraction) and the number of hydrogens are shown below. BPTI Lys Ser Tyr Thr Wat ---------------------------------------------------------# of H 12 1 4 3 112 (4∼) Pol_H 0.39 0.36 1.08 0.20 0.98(0.38) Karplus 0.25 0.71 0.81 0.19 - (0.35) Ornstein 0.22 0.96 0.00 0.07 Ornstn(scaled) 0.51 0.96 1.28 0.07 (1.17) ---------------------------------------------------------internal waters. by random generation

257

11. Miscellaneous RSA Lys Ser Tyr Thr Wat ---------------------------------------------------------# of H 30 15 6 10 256 GuesWatH 0.61 0.96 1.22 0.96 0.98 Karplus 0.60 0.98 0.60 1.12 1.20 Ornstein 0.20 0.61 0.60 0.30 Ornstn(scaled) 0.49 0.89 0.76 0.93 (1.14) ---------------------------------------------------------by random generation 1) A. T. Brunger and M. Karplus, Proteins, 4, 148 (1988). 2) M. B. Bass„, R. L. Ornstein, Proteins, 12, 266 (1992). * The accuracies seem to be similar among three approaches if scaled values of Ornstein’s data are considered.

FILES Default for is "prmtop". The input-pdb-file must have been generated by LEaP or ambpdb, i.e. it must have exactly the same atoms (in the same order) as the prmtop file.

11.5. fantasian A program to evaluate magnetic anisotropy tensor parameters Ivano Bertini Depart. of Chemistry, Univ. of Florence, Florence, Italy e-mail: [email protected]

INPUT FILES:

Observed shifts file (pcshifts.in): 1st 2nd 3rd 4th 5th 6th 7th

column column column column column column column

--> --> --> --> --> --> -->

residue number residue name proton name observed pseudocontact shift value multiplicity of the NMR signal (for example it is 3 for of a methyl gro relative tolerance relative weight

Amber pdb file (parm.pdb): coordinates file in PDB format. If you need to use a solution NMR family of structures you have to superimpose the structures before to use them. OUTPUT FILES:

Observed out file (obs.out): This file is built and read by the program itself, it reports the data read from the input files. output file (res.out): The main output file. In this file the result of the fitting is reported. Using fantasian it is possible to define an internal reference system to visualize the orientation of the

258

11.6. elsize tensor axes. Then in this file you can find PDB format lines (ATOM) which can be included in a PDB file to visualize the internal reference system and the tensor axes. In the main output file all the three equivalent permutations of the tensor parameters with respect to the reference system are reported. The summary of the minimum and maximum errors and that of squared errors are also reported. Example files: in the directory example there are all the files necessary to run a fantasian calculation: fantasian.com --> run file pcshifts.in --> observed shifts file parm.pdb --> coordinate file in PDB format obs.out --> data read from input files res.out --> main output file ~

11.6. elsize NAME

elsize - Given the structure, estimates its effective electrostatic size (parameter

SYNOPSIS Usage: elsize input-pqr-file [-options] -det an estimate based on structural invariants. DEFAULT. -ell an estimate via elliptic integral (numerical). -elf same as above, but via elementary functions. -abc prints semi-axes of the effective ellipsoid. -tab prints all of the above into a table without header. -hea prints same table as -tab but with a header. -deb prints same as -tab with some debugging information. -xyz uses a file containing only XYZ coordinates.

DESCRIPTION

elsize is a program originally written by G. Sigalov to estimate the effective electrostatic size of a structure via a quick, analytical method. The algorithm is presented in detail in Ref. . [68] You will need your structure in a pqr format as input, which can be easily obtained from the prmtop and inpcrd files using ambpdb utility described above: ambpdb -p prmtop -pqr < inpcrd > input-file-pqr

After that you can simply do: elsize input-file-pqr , the value of electrostatic size in Angstroms will be output on stdout. The source code is in the src/etc/ directory, its comments contain more extensive description of the options and give an outline of the algorithm. A somewhat less accurate estimate uses just the XYZ coordinates of the molecule and assumes the default radius size of for all atoms:

259

11. Miscellaneous elsize input-file-xyz

This option is not recommended for very small compounds. The code should not be used on structures made up of two or more completely disjoint" compounds – while the code will still produce a finite value of Arad , it is not very meaningful. Instead, one should obtain estimates for each compound separately.

260

A. Namelist Input Syntax Namelist provides list-directed input, and convenient specification of default values. It dates back to the early 1960’s on the IBM 709, but was regrettably not part of Fortran 77. It is a part of the Fortran 90 standard, and is supported as well by most Fortran 77 compilers (including g77). Namelist input groups take the form: &name var1=value, var2=value, var3(sub)=value, var4(sub,sub,sub)=value,value, var5=repeat*value,value, /

The variables must be names in the Namelist variable list. The order of the variables in the input list is of no significance, except that if a variable is specified more than once, later assignments may overwrite earlier ones. Blanks may occur anywhere in the input, except embedded in constants (other than string constants, where they count as ordinary characters). It is common in older inputs for the ending "/" to be replaced by "&end"; this is non-standardconforming. Letter case is ignored in all character comparisons, but case is preserved in string constants. String constants must be enclosed by single quotes (’). If the text string itself contains single quotes, indicate them by two consecutive single quotes, e.g. C1’ becomes ’C1”’ as a character string constant. Array variables may be subscripted or unsubscripted. An unsubscripted array variable is the same as if the subscript (1) had been specified. If a subscript list is given, it must have either one constant, or exactly as many as the number in the declared dimension of the array. Bounds checking is performed for ALL subscript positions, although if only one is given for a multi-dimension array, the check is against the entire array size, not against the first dimension. If more than one constant appears after an array assignment, the values go into successive locations of the array. It is NOT necessary to input all elements of an array. Any constant may optionally be preceded by a positive (1,2,3,..) integer repeat factor, so that, for example, 25*3.1415 is equivalent to twenty-five successive values 3.1415. The repeat count separator, *, may be preceded and followed by 0 or more blanks. Valid LOGICAL constants are 0, F, .F., .FALSE., 1, T, .T., and .TRUE.; lower case versions of these also work.

261

A. Namelist Input Syntax

262

B. GROUP Specification This section describes the format used to define groups of atoms in various AMBER programs. In sander, a group can be specified as a movable "belly" while the other atoms are fixed absolutely in space (aside from scaling caused by constant pressure simulation), and/or a group of movable atoms can independently restrained (held by a potential) at their positions. In anal, groups can be defined for energy analysis. Except in the analysis module where different groups of atoms are considered with different group numbers for energy decomposition, in all other places the groups of atoms defined are considered as marked atoms to be included for certain types of calculations. In the case of constrained minimization or dynamics, the atoms to be constrained are read as groups with a different weight for each group. Reading of groups is performed by the routine RGROUP, and you are advised to consult it if there is still some ambiguity in the documentation. Input description: - 1 - Title format(20a4) ITITL Group title for identification. Setting ITITL = ’END’ ends group input. ------------------------------------------------------------------------ 1A - Weight format(f) This line is only provided/read when using GROUP input to define restrained atoms. WT The harmonic force constants in kcal/mol-A**2 for the group of atoms for restraining to a reference position. ------------------------------------------------------------------------ 1B - Control to define the group KTYPG , (IGRP(I) , JGRP(I) , I = 1,7) format(a,14i) KTYPG Type of atom selection performed. A molecule can be defined by using only ’ATOM’ or ’RES’, or part of the molecule can be defined by ’ATOM’ and part by ’RES’. ’ATOM’ The group is defined in terms of atom numbers. The atom number list is given in igrp and jgrp. ’RES’ The group is defined in terms of residue numbers. The residue number list is given in igrp and jgrp. ’FIND’ This control is used to make additional conditions (apart from the ’ATOM’ and ’RES’ controls) which a given atom must satisfy to be included in the current group. The conditions are read in the next section (1C) and are terminated by a SEARCH card. Note that the conditions defined by FIND filter any set(s) of atoms defined by the following ATOM/RES instructions. For example, -- group input: select main chain atoms -FIND

263

B. GROUP Specification * * M * SEARCH RES 1 999 END END ’END’ End input for the current group. Followed by either another group definition (starting again with line 1 above), or by a second ’END’ "card", which terminates all group input. IGRP(I) , JGRP(I) The atom or residue pointers. If ktypg .eq. ’ATOM’ all atoms numbered from igrp(i) to jgrp(i) will be put into the current group. If ktypg .eq. ’RES’ all atoms in the residues numbered from igrp(i) to jgrp(i) will be put into the current group. If igrp(i) = 0 the next control card is read. It is not necessary to fill groups according to the numerical order of the residues. In other words, Group 1 could contain residues 40-95 of a protein, Group 2 could contain residues 1-40 and Group 3 could contain residues 96-105. If ktypg .eq. ’RES’, then associating a minus sign with igrp(i) will cause all residues igrp(i) through jgrp(i) to be placed in separate groups. In the analysis modules, all atoms not explicitly defined as members of a group will be combined as a unit in the (n + 1) group, where the (n) group in the last defined group. ------------------------------------------------------------------------ 1C - Section to read atom characteristics ***** Read only if KTYPG = ’FIND’ ***** JGRAPH(I) , JSYMBL(I) , JTREE(I) , JRESNM(I) format(4a) A series of filter specifications are read. Each filter consists of four fields (JGRAPH,JSYMBL,JTREE,JRESNM), and each filter is placed on a separate line. Filter specification is terminated by a line with JGRAPH = ’SEARCH’. A maximum of 10 filters may be specified for a single ’FIND’ command. The union of the filter specifications is applied to the atoms defined by the following ATOM/RES cards. I.e. if an atom satisfies any of the filters, it will be included in the current group. Otherwise, it is not included. For example, to select all non main chain atoms from residues 1 through 999: -- group input: select non main chain atoms -FIND * * S * * * B * * * 3 * * * E * SEARCH RES 1 999 END

264

END ’END’ End input for the current group. Followed by either another The four fields for each filter line are: JGRAPH(I) The atom name of atom to be included. If this and the following three characteristics are satisfied the atom is included in the group. The wild card ’*’ may be used to to indicate that any atom name will satisfy the search. JSYMBL(I) Amber atom type of atom to be included. The wild card ’*’ may be used to indicate that any atom type will satisfy the search. JTREE(I) The tree name (M, S, B, 3, E) of the atom to be included. The wild card ’*’ may be used to indicate that any tree name will satisfy the search. JRESNM(I) The residue name to which the atom has to belong to be included in the group. The wild card ’*’ may be used to indicate that any residue name will satisfy the search. ------------------------------------------------------------------------

Examples: The molecule 18-crown-6 will be used to illustrate the group options. This molecule is composed of six repeating (-CH2-O-CH2-) units. Let us suppose that one created three residues in the PREP unit: CRA, CRB, CRC. Each of these is a (-CH2-O-CH2-) moiety and they differ by their dihedral angles. In order to construct 18-crown-6, the residues CRA, CRB, CRC, CRB, CRC, CRB are linked together during the LINK module with the ring closure being between CRA(residue 1) and CRB(residue 6). Input 1: Title one RES 1 5 END Title two RES 6 END END

Output 1: Group 1 will contain residues 1 through 5 (CRA, CRB, CRC, CRB, CRC) and Group 2 will contain residue 6 (CRB). Input 2: Title one RES 1 5 END Title two ATOM 36 42 END END

Output 2: Group 1 will contain residues 1 through 5 (CRA, CRB, CRC, CRB, CRC) and Group 2 will contain atoms 36 through 42. Coincidentally, atoms 36 through 42 are also all the atoms in residue 6.

265

B. GROUP Specification Input 3: Title one RES -1 6 END END

Output 3: Six groups will be created; Group 1: CRA, Group 2: CRB,..., Group 6: CRB. Input 4: Title one FIND O2 OS M CRA SEARCH RES 1 6 END END

Output 4: Group 1 will contain those atoms with the atom name ’O2’, atom type ’OS’, tree name ’M’ and residue name ’CRA’. Input 5: Title one FIND O2 OS * * SEARCH RES 1 6 END END

Output 5: Group 1 will contain those atoms with the atom name ’O2’, atom type ’OS’, any tree name and any residue name.

266

C. EVB output file specifications This section describes the contents of the EVB output file evbout. The data type of each variable is enclosed in {· · · }, while the size of each array variable is enclosed in [· · · ]. Below are the formatting specifications for the output data: 100 format( A/, A ) 200 format( A/, I8 ) 300 format( A/, 3(2X,I8), 2X, F14.8 ) 400 format( A/, 2I8, F14.8 ) 500 format( A/, 2I8, F14.8, 2X, F14.8 ) 600 format( A/, 3I8, F14.8, 2X, F14.8 ) 888 format( A, 2X, I10, 2X, A, 2X, F20.8 ) 1000 format( A/, (5(2X,F20.8)) )

The EVB output file begins with the following header information: %

'

write(evb_unit,’(/)’) &

(

%

'

write(evb_unit,’(/)’) write(evb_unit, 100) ’ [DYNAMICS TYPE]: ’, trim( adjustl(evb_dyn) ) write(evb_unit,’(/)’) write(evb_unit, 200) ’ [NBEAD]: ’, ncopy write(evb_unit,’(/)’) write(evb_unit,300) ’ [NEVB] [NBIAS] [NTW_EVB] [DT]: ’ & , nevb, nbias, ntw_evb, dt

evb_dyn ncopy nevb nbias ntw_evb dt

: : : : : :

{character*512} EVB dynamics specification. {integer} No. of PIMD slices. Classical EVB ⇒ ncopy = 1. {integer} No. of diabatic states. {integer} No. of biasing potentials included in Vel0 . {integer} No. of MD steps between output to evbout file. {real} MD time step size (ps).

! Output ONLY if performing mapping potential dynamics. do n = 1, nbias write(evb_unit,400) ’ [MAPPING POTENTIAL]: ni, nf, lambda ’ & , bias_ndx(n,1), bias_ndx(n,2), lambda(n) enddo ! Output ONLY if performing umbrella sampling on an energy gap RC. do n = 1, nbias write(evb_unit,500) ’ [NRG_GAP UMBRELLA]: ni, nf, k, ezero ’ & , bias_ndx(n,1), bias_ndx(n,2), k_umb(n), r0_umb(n)

enddo &

( 267

C. EVB output file specifications

bias_ndx(:,:) lambda(:) k0_umb(:) r0_umb(:)

%

: : : :

{integer}, [nbias,2]. Valence bond state index. {real}, [nbias]. Vλ = (1 − λ )Vii + λV f f . {real}, [nbias]. Umbrella force constant. {real}, [nbias]. RC anchor point for umbrella sampling.

! Output ONLY if sampling involves the difference of distances RC. do n = 1, nbias write(evb_unit,600) & ’ [DBONDS UMBRELLA]: iatom, jatom, katom, k, ezero ’ & , dbonds_RC(n)%iatom, dbonds_RC(n)%jatom & , dbonds_RC(n)%katom, k_umb(n), r0_umb(n) enddo ! Output ONLY if sampling involves a distance RC. do n = 1, nbias write(evb_unit,500) ’ [BOND UMBRELLA]: iatom, jatom, k, ezero ’ & , bond_RC(n)%iatom, bond_RC(n)%jatom, k_umb(n), r0_umb(n)

enddo &

dbonds_RC(:)

bond_RC(:)

k0_umb(:) r0_umb(:)

'

(

: {derived type}, [nbias]. %iatom {integer} index of atom involved in ri j . %jatom {integer} index of atom involved in ri j . %katom {integer} index of atom involved in rk j . : {derived type}, [nbias]. %iatom {integer} index of atom involved in ri j . %jatom {integer} index of atom involved in ri j . : {real}, [nbias]. Umbrella force constant. : {real}, [nbias]. RC anchor point for umbrella sampling.

The following data is output every ntw_evb steps: )

*

. 1 2 268

write(evb_unit,’(/)’) write(evb_unit,888) ’{NSTEP}: ’, nstep, ’{TIME}: ’, nstep*dt

nstep nstep*dt

: {integer}. MD step counter. : {real}. Time (ps).

! Output ONLY if the nuclei are NOT quantized. write(evb_unit,’(A)’) write(evb_unit,1000) ’ [EVB MATRIX]’, evb_Hmat%evb_mat(:,:) write(evb_unit,’(A)’) write(evb_unit,1000) ’

[EVB VEC_0]’, evb_Hmat%evb_vec0(:)

evb_Hmat%evb_mat(:,:) evb_Hmat%evb_vec0(:)

+

,

/ 0

: {real},[nevb,nevb]. EVB matrix elements. : {real},[nevb]. ground-state EVB vector.

! Output ONLY if the nuclei are quantized. write(evb_unit,’(A)’) write(evb_unit,1000) ’ [EVB MATRIX]’, evb_matrix(:,:) write(evb_unit,’(A)’) write(evb_unit,1000) ’ [EVB VEC_0^2]’, evb_pop(:) * nbead_inv

3

4



5 6

 . .

: {real},[nevb,nevb]. P1 ∑P 1

evb_matrix(:,:)

#

$

2 : {real},[nevb]. P1 ∑P 1 C0 P .

evb_pop(:)*nbead_inv

! Output if performing ground-state dynamics. write(evb_unit,’(A)’)

nrg_frc(:)

! Output if performing umbrella sampling with nuclear quantization write(evb_unit,’(A)’)

:write(evb_unit,999)

5 6 5 6

Vn1

: {real},[3]. KE + Vel0 , KE, Vel0 in kcal/mol.

! Output if performing umbrella sampling write(evb_unit,’(A)’) write(evb_unit,1000) ’ [RC EVB]’, ( evb_bias%RC(n), n = 1, nbias )

6

.

write(evb_unit,1000) ’{VEL0_PIMD}: ’, ( nrg_frc(n), n = 1, 3 )

9

5

V11

evb_bias%RC(:) nrg_frc(:)

’{VEL0_PIMD}: ’, ( nrg_frc(n), n = 1, 3 )

: {real}.

dVeff /dλ [Eq. (5.36)].

! Output only if out_RCdot = .true. write(evb_unit,’(A)’) write(evb_unit,1000) ’{TST: (d/dt) RC}: ’, RCdot

= = = = : {real}. =ξ˙ = [Eq. (5.15)].

! Output if performing qi_bond_dyn or qi_dbonds_dyn write(evb_unit,’(A)’)

write(evb_unit,1000) ’{QI rate: f_v, F, G}: ’, f_v, F, G

f_v F G

.

···

. . .

Vn

7



  .

8

;

<

7

write(evb_unit,1000) ’{TI MASS: (d/dl) V_eff}: ’, dV_dl

RCdot

..

V1n

: {real},[nbias]. RC value. : {real},[3]. KE + Vel0 , KE, Vel0 in kcal/mol.

! Output if performing TI by mass write(evb_unit,’(A)’)

dV_dl

···

: {real}. fv [Eq. (5.27)]. : {real}. F [Eq. (5.28)]. : {real}. G [Eq. (5.29)].

8

7

8

7

8

269

P

C. EVB output file specifications

270

D. Distributed Gaussian EVB format specifications The distributed Gaussian EVB method in Amber provides native support for the Gaussian [99] formatted checkpoint file. Support for other electronic structure packages is provided via the Amber EVB format. The user will need to write a script that converts outputs from these other electronic structure packages to the Amber EVB format. While the DG EVB method utilizes the internal coordinate representation of the molecular system by default, Cartesian gradient and Hessian information can be used for the DG fitting procedure. Amber has the machinery to automatically transform from Cartesians to internals based on the specified internal coordinate definitions. Both flavors of the EVB formatted ab initio data files utilize the following fixed formatting where applicable (see the read statements below and examples in the test/evb directory):

1000 format( 5( 1PE16.8 ) ) 3000 format( 4I12 )

D.1. Cartesian coordinate representation ) =* > ) * = >

+

[coordinate type]

?, @

use_cartesians

read( ioe, ’(A)’ ) coord_type

coord_type == "use_cartesians"

=> gradient & Hessian in Cartesians

[external evb data dimension] 56

12

13

19

24

read( ioe, ’(5I12)’ ) ncoord, natm, nbond, nangle, ndihed ncoord natm nbond nangle ndihed

: : : : :

total No. of internal coordinates No. of atoms No. of bonds No. of angles No. of proper dihedrals

+

?, @

271

D. Distributed Gaussian EVB format specifications %

[redundant internal indices] . . . 1 2 . . . 2 1 . . . 6 1 . . .

& -

'

0

0

6

0

2

3

( /

do n = 1, nbond + nangle + ndihed read( ioe, 3000 ) i, j, k, l . . . enddo .

5 6 )

i i i

j j j

0 k k

0 0 l

0

: bond between atoms i & j : angle between atoms i, j, & k, with j at apex : proper dihedral, with j & k forming the inner bond

[cartesian coordinates] -2.10145193E+00 3.72231492E-01 . . .

0.00000000E+00

0.00000000E+00

*

read( ioe, 1000 ) ( xdat%qcart(n), n = 1, natm*3) read( ioe, * )

* )

[electronic energy]

) *

5

6 1 2 5 6 ) *

272

7

1.86063791E+00

8 + ,

+

, +

-3.226440399344254E+02

read( ioe, * ) xdat%v read( ioe, * )

[cartesian gradient] 3.17848421E-07 1.39797188E-07 . . .

,

7

6.11516832E-31 -2.06822408E-07 -2.80165145E-07

8 3

read( ioe, 1000 ) ( grad_cart(n), n = 1, natm*3) read( ioe, * )

[cartesian hessian] 4.65149270E-01 1.00394244E-01 . . .

7.54852119E-01 -4.82566443E-17

4

6.87529647E-17

read( ioe, 1000 ) ( ch(n), n = 1, natm*3*(natm*3+1)/2 ) read( ioe, * ) ch(:)

: lower triangle of Cartesian Hessian.

7

8 + ,

D.2. Internal coordinate representation

D.2. Internal coordinate representation ) =* > ) =* >

+

[coordinate type]

?, @

use_internals

read( ioe, ’(A)’ ) coord_type

coord_type == "use_internals"

=> gradient & Hessian in internals

56

12

13

19

24

read( ioe, ’(5I12)’ ) ncoord, natm, nbond, nangle, ndihed ncoord natm nbond nangle ndihed

: : : : :

%

total No. of internal coordinates No. of atoms No. of bonds No. of angles No. of proper dihedrals

[redundant internal indices] . . . 1 2 . . . 2 1 . . . 6 1 . . .

& -

0

0

6

0

2

3

6 ) *

i i i

j j j

0 k k

0 0 l

?, @

'

( /

do n = 1, nbond + nangle + ndihed read( ioe, 3000 ) i, j, k, l . . . enddo .

5

+

[external evb data dimension]

0

: bond between atoms i & j : angle between atoms i, j, & k, with j at apex : proper dihedral, with j & k forming the inner bond

[cartesian coordinates] -2.10145193E+00 3.72231492E-01 . . .

0.00000000E+00

0.00000000E+00

read( ioe, 1000 ) ( xdat%qcart(n), n = 1, natm*3) read( ioe, * )

7

1.86063791E+00

8 + ,

273

D. Distributed Gaussian EVB format specifications 5

6 5 6 ) * ) *

5 6 ) *

5 6 ) *

274

[redundant internal coordinates] 2.57516094E+00 2.54225222E+00 . . .

2.41077005E+00

2.67027840E+00

7

2.43908613E+00

8 7

read( ioe, 1000 ) ( xdat%q(n), n = 1, ncoord ) read( ioe, * ) read_qint = .true.

8

+

[electronic energy]

, +

-3.226440399344254E+02

read( ioe, * ) xdat%v read( ioe, * )

,

[redundant internal gradient] -3.16984808E-07 -1.14744500E-07 -2.60042682E-08 -5.64233681E-08 . . .

7

3.56746392E-08

8 +

read( ioe, 1000 ) ( xdat%d(n), n = 1, ncoord ) read( ioe, * )

[redundant internal hessian] 2.75181669E-01 9.43369526E-03 . . .

4.31679400E-01

5.40885192E-02

,

1.51723420E-03

read( ioe, 1000 ) ( ih(n), n = 1, ncoord*(ncoord+1)/2 ) read( ioe, * ) ih(:)

7

: lower triangle of internal coordinate Hessian.

8 + ,

E. AMBER Trajectory NetCDF Format John Mongan ([email protected])

E.1. Introduction The file format described in this document was developed for storing data generated by molecular dynamics simulations. It was introduced in version 9 of the AMBER suite of programs (http://amber.scripps.edu). The primary design goals of this format are: • Efficient input and output • Compact, high-precision representation of data • Portability of data files across different machine architectures • Extensibility of the format (ability to add additional data without re-writing parsers) • Compatibility with existing tools and formats The file format is based on the NetCDF (Network Common Data Form) developed by Unidata (http://www.unidata.ucar.edu/software/netcdf/). NetCDF is designed for representation of arbitrary array-based data. Unidata provides libraries with bindings in C, C++, Fortran (F77 and F90), Java, Python, Perl, Ruby and MATLAB for reading and writing NetCDF files. The design goals above are largely met by NetCDF and the libraries that implement it. It is expected that all I/O of the format described here will occur through these libraries; this specification describes the file format at a high level in terms of the API implemented by version 3.6 of these libraries. In NetCDF terms, this document is a “Convention,” describing the names, dimensions and attributes of the arrays that may be present in the file.

E.2. Program behavior Programs creating trajectory files (“creators”) shall adhere strictly to the requirements of this document. Programs reading trajectory files (“readers”) shall be as permissive as possible in applying the requirements of this document. Readers may emit warnings if out-of-spec files are encountered; these warnings should include information about the program that originally created the file (see Global attributes, section E.4). Readers shall not fail to read a file unless the required information cannot be located or interpreted. In particular, to ensure forward compatibility with later extensions of the format, readers shall not fail or emit warnings if elements not described in this document are present in the file.

275

E. AMBER Trajectory NetCDF Format

E.3. NetCDF file encoding Trajectory files shall be encoded in the manner employed by NetCDF version 3.x. Those using NetCDF versions 4 or later should take care to ensure that files are read and written using this encoding, and not the HDF5 encoding.

Trajectory files shall use 64 bit offsets This can be accomplished by setting a flag during file creation; refer to API docs for details.

E.4. Global attributes Global attributes shall have type character string. Spelling and capitalization of attribute names shall be exactly as appears below. Creators shall include all attributes marked required and may include attributes marked optional. Creators shall not write an attribute string having a length greater than 80 characters. Readers may warn about missing required attributes, but shall not fail, except in the case of a missing or unexpected Conventions or ConventionVersion attributes.

Conventions (required) Contents of this attribute are a comma or space delimited list of tokens representing all of the conventions to which the file conforms. Creators shall include the string AMBER as one of the tokens in this list. In the usual case, where the file conforms only to this convention, the value of the attribute will simply be “AMBER”. Readers may fail if this attribute is not present or none of the tokens in the list are AMBER. Optionally, if the reader does not expect NetCDF files other than those conforming to the AMBER convention, it may emit a warning and attempt to read the file even when the Conventions attribute is missing.

ConventionVersion (required) Contents are a string representation of the version number of this convention. Future revisions of this convention having the same version number may include definitions of additional variables, dimensions or attributes, but are guaranteed to have no incompatible changes to variables, dimensions or attributes specified in previous revisions. Creators shall set this attribute to “1.0”. If this attribute is present and has a value other than “1.0”, readers may fail or may emit a warning and continue. It is expected that the version of this convention will change rarely, if ever.

application (optional) If the creator is part of a suite of programs or modules, this attribute shall be set to the name of the suite.

276

E.5. Dimensions

program (required) Creators shall set this attribute to the name of the creating program or module.

programVersion (required) Creators shall set this attribute to the preferred textual formatting of the current version number of the creating program or module.

title (optional) Creators may set use this attribute to represent a user-defined title for the data represented in the file. Absence of a title may be indicated by omitting the attribute or by including it with an empty string value.

E.5. Dimensions frame (required, length unlimited) Coordinates along the frame dimension will generally represent data taken from different time steps, but may represent arbitrary conformation numbers when the trajectory file does not represent a true trajectory but rather a collection of conformations (e.g. from clustering).

spatial (required, length 3) This dimension represents the three spatial dimensions (X,Y,Z), in that order.

atom (required, length set as appropriate) Coordinates along this dimension are the indices of particles for which data is stored in the file. The length of this dimension may be different (generally smaller) than the actual number of particles in the simulation if the user chooses to store data for only a subset of particles.

cell_spatial (optional, length 3) This dimension represents the three lengths (a,b,c) that define the size of the unit cell.

cell_angular (optional, length 3) This dimension represents the three angles (alpha,beta,gamma) that define the shape of the unit cell.

label (optional, length set as appropriate) This dimension is used for character strings in label variables where the label is longer than a single character. The length of this dimension is equal to the length of the longest label string.

277

E. AMBER Trajectory NetCDF Format

E.6. Variables Variables are described below as ( [,..]) Note that the order of dimensions corresponds to the CDL and C APIs. When using the Fortran APIs, the order of dimensions should be reversed.

E.6.1. Label variables Label variables shall be written by creators whenever their corresponding dimension is present. These variables are for self-description purposes, so readers may generally ignore them. Labels requiring more than one character per coordinate shall use the label dimension. Individual coordinate labels that are shorter than the length of the label dimension shall be space padded to the length of the label dimension.

char spatial(spatial) Creators shall write the string “xyz” to this variable, indicating the labels for coordinates along the spatial dimension.

char cell_spatial(cell_spatial) Creators shall write the string “abc” to this variable, indicating the labels for the three lengths defining the size of the unit cell.

char cell_angular(cell_angular, label) Creators shall write the strings “alpha”, “beta”, “gamma” to this variable, naming the angles defining the shape of the unit cell.

E.6.2. Data variables All data variables are optional. Some data variables have dependencies on other data variables, as described below. Creators shall define a units attribute of type character string for each variable as described below. Creators may define a scale_factor attribute of type float for each variable. Creators shall ensure that the units of data values, after being multiplied by the value of scale_factor (if it exists) are equal to that described by the units attribute. If a scale_factor attribute exists for a variable, readers shall multiply data values by the value of the scale_factor attribute before interpreting the data. This scaling burden is placed on the reader rather than the creator, as writing data is expected to be a more time-sensitive operation than reading it. It is left as an implementation detail whether creators create a separate file for each variable grouping (e.g. coordinates and velocities) or a single file containing all variables. Some creators may allow the user to select the approach. Readers should support reading both styles, that is, combining data from multiple files or reading it all from a single file.

278

E.7. Example

float time(frame) units = ”picosecond” When coordinates on the frame dimension have a temporal sequence (e.g. they form a molecular dynamics trajectory), creators shall define this dimension and write a float for each frame coordinate representing the number of picoseconds of simulated time elapsed since the start of the trajectory. When the file stores a collection of conformations having no temporal sequence, creators shall omit this variable.

float coordinates(frame, atom, spatial) units = ”angstrom” This variable shall contain the Cartesian coordinates of the specified particle for the specified frame.

float cell_lengths(frame, cell_spatial) units = ”angstrom” When the coordinates variable is included and the data in the coordinates variable come from a simulation with periodic boundaries, creators shall include this variable. This variable shall represent the lengths (a,b,c) of the unit cell for each frame. When each of the angles in cell_angles is 90, a, b and c are parallel to the x, y and z axes, respectively. If the simulation has one or two dimensional periodicity, then the length(s) corresponding to spatial dimensions in which there is no periodicity shall be set to zero.

float cell_angles(frame, cell_angular) units = ”degree” Creators shall include this variable if and only if they include the cell_lengths variable. This variable shall represent the angles (α, β , γ) defining the unit cell for each frame. α defines the angle between the a-b and a-c planes, β defines the angle between the a-b and b-c planes and γ defines the angle between the a-c and b-c planes. Angles that are undefined due to less than three dimensional periodicity shall be set to zero.

float velocities(frame, atom, spatial) units = ”angstrom/picosecond” When the velocities variable is present, it shall represent the cartesian components of the velocity for the specified particle and frame. It is recognized that due to the nature of commonly used integrators in molecular dynamics, it may not be possible for the creator to write a set of velocities corresponding to exactly the same point in time as defined by the time variable and represented in the coordinates variable. In such cases, the creator shall write a set of velocities from the nearest point in time to that represented by the specified frame.

E.7. Example The following is an example of the CDL for a trajectory file conforming to the preceding specification and containing most of the elements described in this document. This CDL was generated using ncdump -h .

279

E. AMBER Trajectory NetCDF Format netcdf mdtrj { dimensions: frame = UNLIMITED ; // (10 currently) spatial = 3 ; atom = 28 ; cell_spatial = 3 ; cell_angular = 3 ; label = 5 ; variables: char spatial(spatial) ; char cell_spatial(cell_spatial) ; char cell_angular(cell_angular, label) ; float time(frame) ; time:units = "picosecond" ; float coordinates(frame, atom, spatial) ; coordinates:units = "angstrom" ; float cell_lengths(frame, cell_spatial) ; cell_lengths:units = "angstrom" ; float cell_angles(frame, cell_angular) ; cell_angles:units = "degree" ; float velocities(frame, atom, spatial) ; velocities:units = "angstrom/picosecond" ; velocities:scale_factor = 20.455f ; // global attributes: :title = "netCDF output test" ; :application = "AMBER" ; :program = "sander" ; :programVersion = "9.0" ; :Conventions = "AMBER" ; :ConventionVersion = "1.0" ; }

E.8. Extensions and modifications Standards and formats are most useful when they are supported widely, and become less useful and more burdensome if they fragment into multiple dialects. If you plan to support additional variables, dimensions or attributes beyond those described here in a publicly released creator or reader program, please contact the author ([email protected]) for inclusion of these elements into a future revision of this document.

E.9. Revision history • Revision A, February 9, 2006: Initial document

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E.9. Revision history • Revision B, February 15, 2006: Better self-description for unit cells in periodic simulations; standards for indicating one and two dimensional periodicity.

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E. AMBER Trajectory NetCDF Format

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Bibliography [1] Dormann, K.L.; Brueckner, R. Variable Synthesis of the Optically Active Thiotetronic Acid Antibiotics Thiolactomycin, Thiotetromycin, and 834-B1. Angew. Chem. Int. Ed., 2007, 46, 1160–1163. [2] Dormann, K.L.; Steinbrecher, T.; Grond, S.; Labahn, A.; Brueckner, R. Undecided. Chemistry (in preparation), 2008. [3] Pearlman, D.A.; Case, D.A.; Caldwell, J.W.; Ross, W.S.; Cheatham, T.E. III; DeBolt, S.; Ferguson, D.; Seibel, G.; Kollman, P. AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules. Comp. Phys. Commun., 1995, 91, 1–41. [4] Case, D.A.; Cheatham, T.; Darden, T.; Gohlke, H.; Luo, R.; Merz, K.M. Jr.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. The Amber biomolecular simulation programs. J. Computat. Chem., 2005, 26, 1668–1688. [5] Ponder, J.W.; Case, D.A. Force fields for protein simulations. Adv. Prot. Chem., 2003, 66, 27–85. [6] Cheatham, T.E. III; Young, M.A. Molecular dynamics simulation of nucleic acids: Successes, limitations and promise. Biopolymers, 2001, 56, 232–256. [7] Harvey, S.; McCammon, J.A. Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge, 1987. [8] Leach, A.R. Molecular Modelling. Principles and Applications, Second Edition. Prentice-Hall, Harlow, England, 2001. [9] Allen, M.P.; Tildesley, D.J. Computer Simulation of Liquids. Clarendon Press, Oxford, 1987. [10] Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications. Second edition. Academic Press, San Diego, 2002. [11] van Gunsteren, W.F.; Weiner, P.K.; Wilkinson, A.J. eds. Computer Simulations of Biomolecular Systems, Vol. 3. ESCOM Science Publishers, Leiden, 1997. [12] Pratt, L.R.; Hummer, G. eds. Simulation and Theory of Electrostatic Interactions in Solution. American Institute of Physics, Melville, NY, 1999. [13] Becker, O.; MacKerell, A.D.; Roux, B.; Watanabe, M. eds. Computational Biochemistry and Biophysics. Marcel Dekker, New York, 2001.

283

Bibliography [14] Vincent, J.J.; Merz, K.M. Jr. A highly portable parallel implementation of AMBER4 using the message passing interface standard. J. Comput. Chem., 1995, 16, 1420–1427. [15] Cheatham, T.E. III; Brooks, B.R.; Kollman, P.A. in Current Protocols in Nucleic Acid Chemistry, pp Sections 7.5, 7.8, 7.9, 7.10. Wiley, New York, 1999. [16] Kopitz, H.; Zivkovic, A.; Engels, J.W.; Gohlke, H. Determinants of the unexpected stability of RNA fluorobenzene self pairs: Unveiling the Janus face of organic fluorine. in preparation, 2008. [17] Wu, X.; Brooks, B.R. Self-guided Langevin dynamics simulation method. Chem. Phys. Lett., 2003, 381, 512–518. [18] Morishita, T. Fluctuation formulas in molecular-dynamics simulations with the weak coupling heat bath. J. Chem. Phys., 2000, 113, 2976. [19] Mudi, A.; Chakravarty, C. Effect of the Berendsen thermostat on the dynamical properties of water. Mol. Phys., 2004, 102, 681–685. [20] Berendsen, H.J.C.; Postma, J.P.M.; van Gunsteren, W.F.; DiNola, A.; Haak, J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys., 1984, 81, 3684–3690. [21] Harvey, S.C.; Tan, R.K.; Cheatham, T.E. III. The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition. J. Comput. Chem., 1998, 19, 726–740. [22] Andrea, T.A.; Swope, W.C.; Andersen, H.C. The role of long ranged forces in determining the structure and properties of liquid water. J. Chem. Phys., 1983, 79, 4576–4584. [23] Andersen, H.C. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys., 1980, 72, 2384–2393. [24] Uberuaga, B.P.; Anghel, M.; Voter, A.F. Synchronization of trajectories in canonical molecular-dynamics simulations: Observation, explanation, and exploitation. J. Chem. Phys., 2004, 120, 6363–6374. [25] Pastor, R.W.; Brooks, B.R.; Szabo, A. An analysis of the accuracy of Langevin and molecular dynamics algorithms. Mol. Phys., 1988, 65, 1409–1419. [26] Loncharich, R.J.; Brooks, B.R.; Pastor, R.W. Langevin dynamics of peptides: The frictional dependence of isomerization rates of N-actylananyl-N’-methylamide. Biopolymers, 1992, 32, 523–535. [27] Izaguirre, J.A.; Catarello, D.P.; Wozniak, J.M.; Skeel, R.D. Langevin stabilization of molecular dynamics. J. Chem. Phys., 2001, 114, 2090–2098. [28] Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H.J.C. Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes. J. Comput. Phys., 1977, 23, 327–341. [29] Miyamoto, S.; Kollman, P.A. SETTLE: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem., 1992, 13, 952–962.

284

Bibliography [30] Ren, P.; Ponder, J.W. Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J. Comput. Chem., 2002, 23, 1497–1506. [31] Ren, P.; Ponder, J.W. Temperature and pressure dependence of the AMOEBA water model. J. Phys. Chem. B, 2004, 108, 13427–13437. [32] Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald–an Nlog(N) method for Ewald sums in large systems. J. Chem. Phys., 1993, 98, 10089–10092. [33] Essmann, U.; Perera, L.; Berkowitz, M.L.; Darden, T.; Lee, H.; Pedersen, L.G. A smooth particle mesh Ewald method. J. Chem. Phys., 1995, 103, 8577–8593. [34] Crowley, M.F.; Darden, T.A.; Cheatham, T.E. III; Deerfield, D.W. II. Adventures in improving the scaling and accuracy of a parallel molecular dynamics program. J. Supercomput., 1997, 11, 255–278. [35] Sagui, C.; Darden, T.A. in Simulation and Theory of Electrostatic Interactions in Solution, Pratt, L.R.; Hummer, G., Eds., pp 104–113. American Institute of Physics, Melville, NY, 1999. [36] Toukmaji, A.; Sagui, C.; Board, J.; Darden, T. Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions. J. Chem. Phys., 2000, 113, 10913– 10927. [37] Sagui, C.; Pedersen, L.G.; Darden, T.A. Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations. J. Chem. Phys., 2004, 120, 73–87. [38] Wu, X.; Brooks, B.R. Isotropic periodic sum: A method for the calculation of long-range interactions. J. Chem. Phys., 2005, 122, 044107. [39] Klauda, J.B.; Wu, X.; Pastor, R.W.; Brooks, B.R. Long-Range Lennard-Jones and Electrostatic Interactions in Interfaces:. J. Phys. Chem. B, 2007, 111, 4393–4400. [40] Takahashi, K.; Yasuoka, K.; Narumi, T. Cutoff radius effect of isotropic periodic sum method for transport. J. Chem. Phys., 2007, 127, 114511. [41] Weiser, J.; Shenkin, P.S.; Still, W.C. Approximate Atomic Surfaces from Linear Combinations of Pairwise Overlaps (LCPO). J. Computat. Chem., 1999, 20, 217–230. [42] Still, W.C.; Tempczyk, A.; Hawley, R.C.; Hendrickson, T. Semianalytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc., 1990, 112, 6127– 6129. [43] Schaefer, M.; Karplus, M. A comprehensive analytical treatment of continuum electrostatics. J. Phys. Chem., 1996, 100, 1578–1599. [44] Edinger, S.R.; Cortis, C.; Shenkin, P.S.; Friesner, R.A. Solvation free energies of peptides: Comparison of approximate continuum solvation models with accurate solution of the Poisson-Boltzmann equation. J. Phys. Chem. B, 1997, 101, 1190–1197.

285

Bibliography [45] Jayaram, B.; Sprous, D.; Beveridge, D.L. Solvation free energy of biomacromolecules: Parameters for a modified generalized Born model consistent with the AMBER force field. J. Phys. Chem. B, 1998, 102, 9571–9576. [46] Cramer, C.J.; Truhlar, D.G. Implicit solvation models: Equilibria, structure, spectra, and dynamics. Chem. Rev., 1999, 99, 2161–2200. [47] Bashford, D.; Case, D.A. Generalized Born models of macromolecular solvation effects. Annu. Rev. Phys. Chem., 2000, 51, 129–152. [48] Onufriev, A.; Bashford, D.; Case, D.A. Modification of the generalized Born model suitable for macromolecules. J. Phys. Chem. B, 2000, 104, 3712–3720. [49] Lee, M.S.; Salsbury, F.R. Jr.; Brooks, C.L. III. Novel generalized Born methods. J. Chem. Phys., 2002, 116, 10606–10614. [50] Dominy, B.N.; Brooks, C.L. III. Development of a generalized Born model parameterization for proteins and nucleic acids. J. Phys. Chem. B, 1999, 103, 3765–3773. [51] Tsui, V.; Case, D.A. Molecular dynamics simulations of nucleic acids using a generalized Born solvation model. J. Am. Chem. Soc., 2000, 122, 2489–2498. [52] Calimet, N.; Schaefer, M.; Simonson, T. Protein molecular dynamics with the generalized Born/ACE solvent model. Proteins, 2001, 45, 144–158. [53] Onufriev, A.; Bashford, D.; Case, D.A. Exploring protein native states and large-scale conformational changes with a modified generalized Born model. Proteins, 2004, 55, 383–394. [54] Srinivasan, J.; Trevathan, M.W.; Beroza, P.; Case, D.A. Application of a pairwise generalized Born model to proteins and nucleic acids: inclusion of salt effects. Theor. Chem. Acc., 1999, 101, 426–434. [55] Onufriev, A.; Case, D.A.; Bashford, D. Effective Born radii in the generalized Born approximation: The importance of being perfect. J. Comput. Chem., 2002, 23, 1297– 1304. [56] Hawkins, G.D.; Cramer, C.J.; Truhlar, D.G. Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium. J. Phys. Chem., 1996, 100, 19824–19839. [57] Richards, F.M. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng., 1977, 6, 151–176. [58] Schaefer, M.; Froemmel, C. A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution. J. Mol. Biol., 1990, 216, 1045–1066. [59] Feig, M.; Onufriev, A.; Lee, M.; Im, W.; Case, D.A.; Brooks, C.L. III. Performance comparison of the generalized Born and Poisson methods in the calculation of the electrostatic solvation energies for protein structures. J. Comput. Chem., 2004, 25, 265–284.

286

Bibliography [60] Hawkins, G.D.; Cramer, C.J.; Truhlar, D.G. Pairwise solute descreening of solute charges from a dielectric medium. Chem. Phys. Lett., 1995, 246, 122–129. [61] Schaefer, M.; Van Vlijmen, H.W.T.; Karplus, M. Electrostatic contributions to molecular free energies in solution. Adv. Protein Chem., 1998, 51, 1–57. [62] Tsui, V.; Case, D.A. Theory and applications of the generalized Born solvation model in macromolecular simulations. Biopolymers (Nucl. Acid. Sci.), 2001, 56, 275–291. [63] Sosa, C.P.; Hewitt, T.; Lee, M.S.; Case, D.A. Vectorization of the generalized Born model for molecular dynamics on shared-memory computers. J. Mol. Struct. (Theochem), 2001, 549, 193–201. [64] Roe, D.R.; Okur, A.; Wickstrom, L.; Hornak, V.; Simmerling, C. Secondary Structure Bias in Generalized Born Solvent Models: Comparison of Conformational Ensembles and Free Energy of Solvent Polarization from Explicit and Implicit Solvation. J. Phys. Chem. B, 2007, 111, 1846–1857. [65] Mongan, J.; Simmerling, C.; A. McCammon, J.; A. Case, D.; Onufriev, A. Generalized Born with a simple, robust molecular volume correction. J. Chem. Theory Comput., 2006, 3, 156–169. [66] Sitkoff, D.; Sharp, K.A.; Honig, B. Accurate calculation of hydration free energies using macroscopic solvent models. J. Phys. Chem., 1994, 98, 1978–1988. [67] Sigalov, G.; Scheffel, P.; Onufriev, A. Incorporating variable environments into the generalized Born model. J. Chem. Phys., 2005, 122, 094511. [68] Sigalov, G.; Fenley, A.; Onufriev, A. Analytical electrostatics for biomolecules: Beyond the generalized Born approximation . J. Chem. Phys., 2006, 124, 124902. [69] Luo, R.; David, L.; Gilson, M.K. Accelerated Poisson-Boltzmann calculations for static and dynamic systems. J. Comput. Chem., 2002, 23, 1244–1253. [70] Lu, Q.; Luo, R. A Poisson-Boltzmann dynamics method with nonperiodic boundary condition. J. Chem. Phys., 2003, 119, 11035–11047. [71] Honig, B.; Nicholls, A. Classical electrostatics in biology and chemistry. Science, 1995, 268, 1144–1149. [72] Sharp, K.A.; Honig, B. Electrostatic interactions in macromolecules: Theory and experiment. Annu. Rev. Biophys. Biophys. Chem., 1990, 19, 301–332. [73] Davis, M.E.; McCammon, J.A. Electrostatics in biomolecular structure and dynamics. Chem. Rev., 1990, 90, 509–521. [74] Gilson, M.K.; Sharp, K.A.; Honig, B.H. Calculating the electrostatic potential of molecules in solution: method. J. Comput. Chem., 1988, 9, 327–35. [75] Warwicker, J.; Watson, H.C. Calculation of the electric potential in the active site cleft due to. J. Mol. Biol., 1982, 157, 671–679.

287

Bibliography [76] Klapper, I.; Hagstrom, R.; Fine, R.; Sharp, K.; Honig, B. Focussing of electric fields in the active stie of Cu, Zn superoxide dismutase. Proteins, 1986, 1, 47–59. [77] Tan, C. H.; Tan, Y. H.; Luo, R. Implicit nonpolar solvent models. J. Phys. Chem. B, 2007, 111, 12263–12274. [78] Gallicchio, E.; Kubo, M.M.; Levy, R.M. Enthalpy-entropy and cavity decomposition of alkane hydration free energies: Numerical results and implications for theories of hydrophobic solvation. J. Phys. Chem., 2000, 104, 6271–6285. [79] Floris, F.; Tomasi, J. Evaluation of the dispersion contribution to the solvation energy. A simple computational model in the continuum approximation. J. Comput. Chem., 1989, 10, 616–627. [80] Davis, M.E.; McCammon, J.A. Solving the finite-difference linearized PoissonBoltzmann equation – a comparison of relaxation and conjugate gradient methods. J. Comput. Chem., 1989, 10, 386–391. [81] Nicholls, A.; Honig, B. A rapid finite difference algorithm, utilizing successive overrelaxation to solve the Poisson-Boltzmann equation. J. Comput. Chem., 1991, 12, 435– 445. [82] Bashford, D. An object-oriented programming suite for electrostatic effects in biological molecules. Lect. Notes Comput. Sci., 1997, 1343, 233–240. [83] Davis, M.E.; McCammon, J.A. Dielectric boundary smoothing in finite difference solutions of the Poisson equation: An approach to improve accuracy and convergence. J. Comput. Chem., 1991, 12, 909–912. [84] Luty, B.A.; Davis, M.E.; McCammon, J.A. Electrostatic energy calculations by a finitedifference method: Rapid calculation of charge-solvent interaction energies. J. Comput. Chem., 1992, 13, 768–771. [85] Tan, C. H.; Yang, L. J.; Luo, R. How well does Poisson-Boltzmann implicit solvent agree with explicit solvent? A quantitative analysis. J. Phys. Chem. B, 2006, 110, 18680– 18687. [86] Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions. John Wiley and Sons, New York, 1991. [87] Billeter, S.R.; Webb, S.P.; Iordanov, T.; Agarwal, P.K.; Hammes-Schiffer, S. Hybrid approach for including electronic and nuclear quantum effects in molecular dynamics simulations of hydrogen transfer reactions in enzymes. J. Chem. Phys., 2001, 114, 6925. [88] Schlegel, H.B.; Sonnenberg, J.L. Empirical valence-bond models for reactive potential energy surfaces using distributed Gaussians. J. Chem. Theory Comput., 2006, 2, 905. [89] Sonnenberg, J.L.; Schlegel, H.B. Empirical valence bond models for reactive potential energy surfaces. II. Intramolecular proton transfer in pyridone and the Claisen reaction of allyl vinyl ether. Mol. Phys., 2007, 105, 2719.

288

Bibliography [90] Saad, Y.; Schultz, M.H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 1986, 7, 856. [91] Pulay, P. Convergence acceleration of iterative sequencies. The case of SCF iteration. Chem. Phys. Lett., 1980, 73, 393. [92] Pulay, P. Improved SCF convergence acceleration. J. Comput. Chem., 1982, 3, 556. [93] Feynman, R.P.; Hibbs, A.R. Quantum Mechanics and Path Integrals. McGraw-Hill, New York, 1965. [94] Feynman, R.P. Statistcal Mechanics. Benjamin, Reading, MA, 1972. [95] Kleinert, H. Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics. World Scientific, Singapore, 1995. [96] Kumar, S.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A.; Rosenberg, J.M. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comput. Chem., 1992, 13, 1011–1021. [97] Kumar, S.; Rosenberg, J.M.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A. Multidimensional free-energy calculations using the weighted histogram analysis method. J. Comput. Chem., 1995, 16, 1339–1350. [98] Roux, B. The calculation of the potential of mean force using computer simulations. Comput. Phys. Comm., 1995, 91, 275–282. [99] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A. Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02. Gaussian, Inc., Wallingford, CT, 2004. [100] Rappe, A.K.; Casewit, C.J.; Colwell, K.S.; Goddard III, W.A.; Skiff, W.M. UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc., 1992, 114, 10024–10035. [101] Ren, P.Y.; Ponder, J.W. Polarizable atomic multipole water model for molecular mechanics simulation. J. Phys. Chem. B, 2003, 107, 5933–5947. [102] Ren, P.Y.; Ponder, J.W. Tinker polarizable atomic multipole force field for proteins. to be published., 2006.

289

Bibliography [103] Stewart, J.J.P. Optimization of parameters for semiempirical methods I. Method. J. Comput. Chem., 1989, 10, 209–220. [104] Dewar, M.J.S.; Zoebisch, E.G.; Healy, E.F.; Stewart, J.J.P. AM1: A new general purpose quantum mechanical molecular model. J. Am. Chem. Soc., 1985, 107, 3902–3909. [105] Rocha, G.B.; Freire, R.O.; Simas, A.M.; Stewart, J.J.P. RM1: A Reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br and I. J. Comp. Chem., 2006, 27, 1101–1111. [106] Dewar, M.J.S.; Thiel, W. Ground states of molecules. 38. The MNDO method, approximations and parameters. J. Am. Chem. Soc., 1977, 99, 4899–4907. [107] Repasky, M.P.; Chandrasekhar, J.; Jorgensen, W.L. PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods. J. Comput. Chem., 2002, 23, 1601–1622. [108] McNamara, J.P.; Muslim, A.M.; Abdel-Aal, H.; Wang, H.; Mohr, M.; Hillier, I.H.; Bryce, R.A. Towards a quantum mechanical force field for carbohydrates: A reparameterized semiempirical MO approach. Chem. Phys. Lett., 2004, 394, 429–436. [109] Seabra, G.M.; Walker, R.C.; Elstner, M.; Case, D.A.; Roitberg, A.E. Implementation of the SCC-DFTB Method for Hybrid QM/MM Simulations within the Amber Molecular Dynamics Package. J. Phys. Chem. A., 2007, 20, 5655–5664. [110] Porezag, D.; Frauenheim, T.; Kohler, T.; Seifert, G.; Kaschner, R. Construction of tightbinding-like potentials on the basis of density-functional-theory: Applications to carbon. Phys. Rev. B, 1995, 51, 12947. [111] Seifert, G.; Porezag, D.; Frauenheim, T. Calculations of molecules, clusters and solids with a simplified LCAO-DFT-LDA scheme. Int. J. Quantum Chem., 1996, 58, 185. [112] Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent charge density functional tight-binding method for simulation of complex material properties. Phys. Rev. B, 1998, 58, 7260. [113] Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: a density-functional-theory based treatment. J. Chem. Phys., 2001, 114, 5149. [114] Kalinowski, J.A.; Lesyng, B.; Thompson, J.D.; Cramer, C.J.; Truhlar, D.G. Class IV charge model for the self-consistent charge density-functional tight-binding method. J. Phys. Chem. A, 2004, 108, 2545–2549. [115] Walker, R.C.; Crowley, M.F.; Case, D.A. The implementation of a fast and efficient hybrid QM/MM potential method within The Amber 9.0 sander module. J. Computat. Chem., 2008, 29, 1019–1031. [116] Pellegrini, E.; J. Field, M. A generalized-Born solvation model for macromolecular hybrid-potential calculations. J. Phys. Chem. A., 2002, 106, 1316–1326. [117] Nam, K.; Gao, J.; York, D. An efficient linear-scaling Ewald method for long-range electrostatic interactions in combined QM/MM calculations. J. Chem. Theory Comput., 2005, 1, 2–13.

290

Bibliography [118] Kruger, T.; Elstner, M.; Schiffels, P.; Frauenheim, T. Validation of the density-functional based tight-binding approximation. J. Chem. Phys., 2005, 122, 114110. [119] Kollman, P. Free energy calculations: Applications to chemical and biochemical phenomena. Chem. Rev., 1993, 93, 2395–2417. [120] Simonson, T. in Computational Biochemistry and Biophysics, Becker, O.; MacKerell, A.D.; Roux, B.; Watanabe, M., Eds. Marcel Dekker, New York, 2001. [121] Steinbrecher, T.; Case, D.A.; Labahn, A. A multistep approach to structure-based drug design: Studying ligand binding at the human neutrophil elastase. J. Med.. Chem., 2006, 49, 1837–1844. [122] Steinbrecher, T.; Hrenn, A.; Dormann, K.; Merfort, I.; Labahn, A. Bornyl (3,4,5trihydroxy)-cinnamate - An optimized human neutrophil elastase inhibitor designed by free energy calculations. Bioorg. Med. Chem., 2008, in press. [123] Hummer, G.; Szabo, A. Calculation of free-energy differences from computer simulations of initial and final states. J. Chem. Phys., 1996, 105, 2004–2010. [124] Steinbrecher, T.; Mobley, D.L.; Case, D.A. Non-linear scaling schemes for LennardJones interactions in free energy calculations. J. Chem. Phys., 2007, 127, 214108. [125] Deng, Y.; Roux, B. Calculation of standard binding free energies: Aromatic molecules in the T4 lysozyme L99A mutant. J. Chem. Theor. Comput., 2006, 2, 1255–1273. [126] Valleau, J.P.; Torrie, G.M. in Modern Theoretical Chemistry, Vol. 5: Statistical Mechanics, Part A,, Berne, B.J., Ed. Plenum Press, New York, 1977. [127] Kottalam, J.; Case, D.A. Dynamics of ligand escape from the heme pocket of myoglobin. J. Am. Chem. Soc., 1988, 110, 7690–7697. [128] Kästner, J.; Thiel, W. Bridiging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration". J. Chem. Phys., 2005, 123, 144104. [129] Jensen, M.O.; Park, S.; d, E.Tajkhorshi; Schulten, K. Energetics of glycerol conduction through aquaglyceroporin GlpF. Proc. Natl. Acad. Sci. USA, 2002, 99, 6731–6736. [130] Crespo, A.; Marti, M.A.; Estrin, D.A.; Roitberg, A.E. Multiple-steering QM-MM calculation of the free energy profile in chorismate mutase. J. Am. Chem. Soc., 2005, 127, 6940–6941. [131] Jarzynski, C. Nonequilibrium equality for free energy differences. Phys. Rev. Lett., 1997, 78, 2690–2693. [132] Hummer, G.; Szabo, A. Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA, 2001, 98, 3658. [133] Hummer, G.; Szabo, A. Kinetics from nonequilibrium single-molecule pulling experiments. Biophys. J., 2003, 85, 5–15.

291

Bibliography [134] Mitsutake, A.; Sugita, Y.; Okamoto, Y. Generalized-ensemble algorithms for molecular simulations of biopolymers. Biopolymers, 2001, 60, 96–123. [135] Nymeyer, H.; Gnanakaran, S.; García, A.E. Atomic simulations of protein folding using the replica exchange algorithm. Meth. Enzymol., 2004, 383, 119–149. [136] Cheng, X.; Cui, G.; Hornak, V.; Simmerling, C. Modified replica exchange simulation methods for local structure refinement. J. Phys. Chem. B, 2005, 109, 8220–8230. [137] Okur, A.; Wickstrom, L.; Layten, M.; Geney, R.; Song, K.; Hornak, V.; Simmerling, C. Improved efficiency of replica exchange simulations through use of a hybrid explicit/implicit solvation model. J. Chem. Theory Comput., 2006, 2, 420–433. [138] Okur, A.; Wickstrom, L.; Simmerling, C. Evaluation of salt bridge structure and energetics in peptides using explicit, implicit and hybrid solvation models. J. Chem. Theory Comput., 2008, 4, 488–498. [139] Okur, A.; Roe, D.R.; Cui, G.; Hornak, V.; Simmerling, C. Improving convergence of replica-exchange simulations through coupling to a high-temperature structure reservoir. J. Chem. Theory comput., 2007, 3, 557–568. [140] Roitberg, A.E.; Okur, A.; Simmerling, C. Coupling of replica exchange simulations to a non-Boltzmann structure reservoir. J. Phys. Chem. B, 2007, 111, 2415–2418. [141] Babin, V.; Roland, C.; Sagui, C. Adaptively biased molecular dynamics for free energy calculations. J. Chem. Phys., 2008, 128, X–X. [142] Huber, Thomas; Torda, Andrew E.; van Gunsteren, Wilfred F. Local elevation: a method for improving the searching properties of molecular dynamics simulation. J. Comput. Aided. Mol. Des., 1994, 8, 695–708. [143] Wang, Fugao; Landau, D. P. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett., Mar 2001, 86(10), 2050–2053. [144] Darve, Eric; Pohorille, Andrew. Calculating free energies using average force. J. Chem. Phys., 2001, 115(20), 9169–9183. [145] Laio, A.; Parrinello, M. Escaping free-energy minima. Proc. Natl. Acad. Sci., 2002, 99, 12562–12566. [146] Iannuzzi, M.; Laio, A.; Parrinello, M. Efficient exploration of reactive potential energy surfaces using car-parrinello molecular dynamics. Phys. Rev. Lett., 2003, 90, 238302–1. [147] Lelièvre, Tony; Rousset, Mathias; Stoltz, Gabriel. Computation of free energy profiles with parallel adaptive dynamics. J. Chem. Phys., 2007, 126, 134111. [148] Raiteri, Paolo; Laio, Alessandro; Gervasio, Francesco Luigi; Micheletti, Cristian; Parrinello, Michele. Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics. J. Phys. Chem., 2006, 110, 3533–3539. [149] Sugita, Yuji; Kitao, Akio; Okamoto, Yuko. Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys., 2000, 113(15), 6042–6051.

292

Bibliography [150] Bussi, Giovanni; Gervasio, Francesco Luigi; Laio, Alessandro; Parrinello, Michele. Free-energy landscape for β hairpin folding from combined parallel tempering and metadynamics. J. Am. Chem. Soc., 2006, 128, 13435–13441. [151] Piana, S.; Laio, A. A bias-exchange approach to protein folding. J. Phys. Chem. B, 2007, 111, 4553–4559. [152] Coutsias, E. A.; Seok, C.; Dill, K. A. Using quaternions to calculate RMSD. J. Comput. Chem., 2004, 25(15), 1849–1857. [153] Park, Sanghyun; Khalili-Araghi, Fatemeh; Tajkhorshid, Emad; Schulten, Klaus. Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality. J. Chem. Phys., 2003, 119(6), 3559–3566. [154] Matsumoto, Makoto; Nishimura, Takuji. Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul., 1998, 8(1), 3–30. [155] Mills, G.; Jónsson, H. Quantum and thermal effects in H2 dissociative adsorption: Evaluation of free energy barriers in multidimensional quantum systems. Phys. Rev. Lett., 1994, 72, 1124–1127. [156] Jónsson, H.; Mills, G.; Jacobsen, K.W. in Classical and Quantum Dynamics in Condensed Phase Simulations, Berne, B.J.; Ciccoti, G.; Coker, D.F., Eds., pp 385–404. World Scientific, Singapore, 1998. [157] Elber, R.; Karplus M, M. A method for determining reaction paths in large molecules: Application to myoglobin. Chem. Phys. Lett., 1987, 139, 375–380. [158] Henkelman, G.; Jónsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys., 2000, 113, 9978–9985. [159] Henkelman, G.; Uberuaga, B.P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys., 2000, 113, 9901–9904. [160] Chu, J.; Trout, B.L.; Brooks, B.R. A super-linear minimization scheme for the nudged elastic band method. J. Chem. Phys., 2003, 119, 12708–12717. [161] Mathews, D.H.; Case, D.A. Nudged Elastic Band calculation of minimal energy pathways for the conformational change of a GG mismatch. J. Mol. Biol., 2006, 357, 1683– 1693. [162] Mongan, J.; Case, D.A.; McCammon, J.A. Constant pH molecular dynamics in generalized Born implicit solvent. J. Comput. Chem., 2004, 25, 2038–2048. [163] Kolossváry, I.; Guida, W.C. Low mode search. An efficient, automated computational method for conformational analysis: Application to cyclic and acyclic alkanes and cyclic peptides. J. Am. Chem. Soc., 1996, 118, 5011–5019.

293

Bibliography [164] Kolossváry, I.; Guida, W.C. Low-mode conformatinoal search elucidated: Application to C39 H80 and flexible docking of 9-deazaguanine inhibitors into PNP. J. Comput. Chem., 1999, 20, 1671–1684. [165] Kolossváry, I.; Keserü, G.M. Hessian-free low-mode conformational search for largescale protein loop optimization: Application to c-jun N-terminal kinase JNK3. J. Comput. Chem., 2001, 22, 21–30. [166] Keserü, G.M.; Kolossváry, I. Fully flexible low-mode docking: Application to induced fit in HIV integrase. J. Am. Chem. Soc., 2001, 123, 12708–12709. [167] Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York, 1989. [168] Liu, D.C.; Nocedal, J. On the limited memory method for large scale optimization. Math. Programming B, 1989, 45, 503–528. [169] Nocedal, J.; L. Morales, J. Automatic preconditioning by limited memory quasi-Newton updating. SIAM J. Opt., 2000, 10, 1079–1096. [170] Schulman, L.S. Techniques and Applications of Path Integration. Wiley & Sons, New York, 1996. [171] Chandler, D.; Wolynes, P.G. Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids. J. Chem. Phys., 1981, 74, 4078– 4095. [172] Ceperley, D.M. Path integrals in the theory of condensed helium. Rev. Mod. Phys., 1995, 67, 279–355. [173] Martyna, G.J.; Klein, M.L.; Tuckerman, M. Nosé-Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys., 1992, 97, 2635. [174] Berne, B.J.; Thirumalai, D. On the simulation of quantum systems: path integral methods. Annu. Rev. Phys. Chem., 1986, 37, 401. [175] Cao, J.; Berne, B.J. On energy estimators in path integral Monte Carlo simulations: Dependence of accuracy on algorithm. J. Chem. Phys., 1989, 91, 6359–6366. [176] Paesani, F.; Zhang, W.; Case, D.A.; Cheatham, T.E.; Voth, G.A. An accurate and simple quantum model for liquid water. J. Chem. Phys., 2006, 125, 184507. [177] Martyna, G.J.; Hughes, A.; Tuckerman, M.E. Molecular dynamics algorithms for path integrals at constant pressure. J. Chem. Phys., 1999, 110, 3275. [178] Voth, G.A. Path-integral centroid methods in quantum statistcal mechanics and dynamics. Adv. Chem. Phys., 1996, 93, 135. [179] Craig, I.R.; Manolopoulos, D.E. Quantum statistics and classical mechnanics: Real time correlation functions from ring polymer molecular dynamics. J. Chem. Phys., 2004, 121, 3368.

294

Bibliography [180] Cao, J.; Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. IV. Algorithms for centroid molecular dynamics. J. Chem. Phys., 1994, 101, 6168. [181] Miller, T.F.; Manolopoulos, D.E. Quantum diffusion in liquid water from ring polymer molecular dynamics. J. Chem. Phys., 2005, 123, 154504. [182] Voth, G.A.; Chandler, D.; Miller, W.H. Rigorous Formulation of Quantum Transition State Theory and Its Dynamical Corrections. J. Chem. Phys., 1989, 91, 7749–7760. [183] Miller, W.H. Semiclassical limit of quantum mechanical transition state theory for nonseparable systems. J. Chem. Phys., 1975, 62, 1899. [184] Miller, W.H.; Zhao, Y.; Ceotto, M.; Yang, S. Quantum instanton approximation for thermal rate constants of chemical. J. Chem. Phys., 2003, 119, 1329–1342. [185] Yamamoto, T.; Miller, W.H. On the efficient path integral evaluation of thermal rate constants with the quantum instanton approximation. J. Chem. Phys., 2004, 120, 3086– 3099. [186] Miller, W.H.; Schwartz, S.D.; Tromp, J.W. Quantum mechanical rate constants for bimolecular reactions. J. Chem. Phys., 1983, 79, 4889–4898. [187] Vaníˇcek, J.; Miller, W.H.; Castillo, J.F.; Aoiz, F.J. Quantum-instanton evalution of the kinetic isotope effects. J. Chem. Phys., 2005, 123, 054108. [188] Vaníˇcek, J.; Miller, W.H. Efficient estimators for quantum instanton evaluation of the kinetic isotope effects: application to the intramolecular hydrogen transfer in pentadiene. J. Chem. Phys., 2007, 127, 114309. [189] Yamamoto, T.; Miller, W.H. Path integral evaluation of the quantum instanton rate constant for proton transfer in a polar solvent. J. Chem. Phys., 2005, 122, 044106. [190] Duggan, B.M.; Legge, G.B.; Dyson, H.J.; Wright, P.E. SANE (Structure Assisted NOE Evaluation): An automated model-based approach for NOE assignment. J. Biomol. NMR, 2001, 19, 321–329. [191] Kalk, A.; Berendsen, H.J.C. Proton magnetic relaxation and spin diffusion in proteins. J. Magn. Reson., 1976, 24, 343–366. [192] Olejniczak, E.T.; Weiss, M.A. Are methyl groups relaxation sinks in small proteins? J. Magn. Reson., 1990, 86, 148–155. [193] Cross, K.J.; Wright, P.E. Calibration of ring-current models for the heme ring. J. Magn. Reson., 1985, 64, 220–231. [194] Ösapay, K.; Case, D.A. A new analysis of proton chemical shifts in proteins. J. Am. Chem. Soc., 1991, 113, 9436–9444. [195] Case, D.A. Calibration of ring-current effects in proteins and nucleic acids. J. Biomol. NMR, 1995, 6, 341–346.

295

Bibliography [196] Banci, L.; Bertini, I.; Gori-Savellini, G.; Romagnoli, A.; Turano, P.; Cremonini, M.A.; Luchinat, C.; Gray, H.B. Pseudocontact shifts as constraints for energy minimization and molecular dynamics calculations on solution structures of paramagnetic metalloproteins. Proteins, 1997, 29, 68. [197] Sanders, C.R. II; Hare, B.J.; Howard, K.P.; Prestegard, J.H. Magnetically-oriented phospholipid micelles as a tool for the study of membrane-associated molecules. Prog. NMR Spectr., 1994, 26, 421–444. [198] Tsui, V.; Zhu, L.; Huang, T.H.; Wright, P.E.; Case, D.A. Assessment of zinc finger orientations by residual dipolar coupling constants. J. Biomol. NMR, 2000, 16, 9–21. [199] Case, D.A. Calculations of NMR dipolar coupling strengths in model peptides. J. Biomol. NMR, 1999, 15, 95–102. [200] Gippert, G.P.; Yip, P.F.; Wright, P.E.; Case, D.A. Computational methods for determining protein structures from NMR data. Biochem. Pharm., 1990, 40, 15–22. [201] Case, D.A.; Wright, P.E. in NMR in Proteins, Clore, G.M.; Gronenborn, A., Eds., pp 53–91. MacMillan, New York, 1993. [202] Case, D.A.; Dyson, H.J.; Wright, P.E. Use of chemical shifts and coupling constants in nuclear magnetic resonance structural studies on peptides and proteins. Meth. Enzymol., 1994, 239, 392–416. [203] Brüschweiler, R.; Case, D.A. Characterization of biomolecular structure and dynamics by NMR cross-relaxation. Prog. NMR Spectr., 1994, 26, 27–58. [204] Case, D.A. The use of chemical shifts and their anisotropies in biomolecular structure determination. Curr. Opin. Struct. Biol., 1998, 8, 624–630. [205] Torda, A.E.; Scheek, R.M.; VanGunsteren, W.F. Time-dependent distance restraints in molecular dynamics simulations. Chem. Phys. Lett., 1989, 157, 289–294. [206] Pearlman, D.A.; Kollman, P.A. Are time-averaged restraints necessary for nuclear magnetic resonance refinement? A model study for DNA. J. Mol. Biol., 1991, 220, 457–479. [207] Torda, A.E.; Brunne, R.M.; Huber, T.; Kessler, H.; van Gunsteren, W.F. Structure refinement using time-averaged J-coupling constant restraints. J. Biomol. NMR, 1993, 3, 55–66. [208] Pearlman, D.A. How well to time-averaged J-coupling restraints work? J. Biomol. NMR, 1994, 4, 279–299. [209] Pearlman, D.A. How is an NMR structure best defined? An analysis of molecular dynamics distance-based approaches. J. Biomol. NMR, 1994, 4, 1–16. [210] Brünger, A.T.; Adams, P.D.; Clore, G.M.; Delano, W.L.; Gros, P.; Grosse-Kunstleve, R.W.; Jiang, J.-S.; Kuszewski, J.; Nilges, M.; Pannu, N.S.; Read, R.J.; Rice, L.M.; Simonson, T.; Warren, G.L. Crystallography and NMR system (CNS): A new software system for macromolecular structure determination. Acta Cryst. D, 1998, 54, 905–921.

296

Bibliography [211] Yu, N.; Yennawar, H.P.; Merz, K.M. Jr. Refinement of protein crystal structures using energy restraints derived from linear-scaling quantum mechanics . Acta Cryst. D, 2005, 61, 322–332. [212] Yu, N.; Li, X.; Cui, G.; Hayik, S.; Merz, K.M. Jr. Critical assessment of quantum mechanics based energy restraints in protein crystal structure refinement. Prot. Sci., 2006, 15, 2773–2784. [213] Yang, W.; Lee, T.-S. A density-matrix divide-and-conquer approach for electronic structure calculations of large molecules. J. Chem. Phys., 1995, 103, 5674–5678. [214] Dixon, S.L.; Merz, K.M. Jr. Semiempirical molecular orbital calculations with linear system size scaling. J. Chem. Phys., 1996, 104, 6643–6649. [215] Dixon, S.L.; Merz, K.M. Jr. Fast, accurate semiempirical molecular orbital calculations for macromolecules. J. Chem. Phys., 1997, 107, 879–893. [216] Connolly, M.L. Analytical molecular surface calculation. J. Appl. Cryst., 1983, 16, 548–558. [217] Srinivasan, J.; Cheatham, T.E. III; Cieplak, P.; Kollman, P.; Case, D.A. Continuum solvent studies of the stability of DNA, RNA, and phosphoramidate–DNA helices. J. Am. Chem. Soc., 1998, 120, 9401–9409. [218] Kollman, P.A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W.; Donini, O.; Cieplak, P.; Srinivasan, J.; Case, D.A.; Cheatham, T.E. III. Calculating structures and free energies of complex molecules: Combining molecular mechanics and continuum models. Accts. Chem. Res., 2000, 33, 889–897. [219] Wang, W.; Kollman, P. Free energy calculations on dimer stability of the HIV protease using molecular dynamics and a continuum solvent model. J. Mol. Biol., 2000, 303, 567. [220] Reyes, C.; Kollman, P. Structure and thermodynamics of RNA-protein binding: Using molecular dynamics and free energy analyses to calculate the free energies of binding and conformational change. J. Mol. Biol., 2000, 297, 1145–1158. [221] Lee, M.R.; Duan, Y.; Kollman, P.A. Use of MM-PB/SA in estimating the free energies of proteins: Application to native, intermediates, and unfolded vilin headpiece. Proteins, 2000, 39, 309–316. [222] Wang, J.; Morin, P.; Wang, W.; Kollman, P.A. Use of MM-PBSA in reproducing the binding free energies to HIV-1 RT of TIBO derivatives and predicting the binding mode to HIV-1 RT of efavirenz by docking and MM-PBSA. J. Am. Chem. Soc., 2001, 123, 5221–5230. [223] Marinelli, L.; Cosconati, S.; Steinbrecher, T.; Limongelli, V.; Bertamino, A.; Novellino, E.; Case, D.A. Homology Modeling of NR2B Modulatory Domain of NMDA Receptor and Analysis of Ifenprodil Binding. ChemMedChem, 2007, 2,, 1498–1510. [224] Miranker, A.; Karplus, M. Functionality maps of binding sites: A multiple copy simultaneous search method. Proteins: Str. Funct. Gen., 1991, 11, 29–34.

297

Bibliography [225] Cheng, X.; Hornak, V.; Simmerling, C. Improved conformational sampling through an efficient combination of mean-field simulation approaches. J. Phys. Chem. B, 2004, 108. [226] Simmerling, C.; Fox, T.; Kollman, P.A. Use of Locally Enhanced Sampling in Free Energy Calculations: Testing and Application of the alpha to beta Anomerization of Glucose. J. Am. Chem. Soc., 1998, 120, 5771–5782. [227] Straub, J.E.; Karplus, M. Enery partitioning in the classical time-dependent Hartree approximation. J. Chem. Phys., 1991, 94, 6737. [228] Ulitsky, A.; Elber, R. The thermal equilibrium aspects of the time-dependent Hartree and the locally enhanced sampling approximations: Formal properties, a correction, and computational examples for rare gas clusters. J. Chem. Phys., 1993, 98, 3380. [229] Storer, J.W.; Giesen, D.J.; Cramer, C.J.; Truhlar, D.G. Class IV charge models: A new semiempirical approach in quantum chemistry. J. Comput.-Aided Mol. Design, 1995, 9, 87–110. [230] Li, J.; Cramer, C.J.; Truhlar, D.G. New class IV charge model for extracting accurate partial charges from Wave Functions. J. Phys. Chem. A., 1998, 102, 1820–1831. [231] Mitin, A.V. The dynamic level shift method for improving the convergence of the SCF procedure. J. Comput. Chem., 1988, 9, 107–110. [232] Ermolaeva, M.D.; van der Vaart, A.; Merz, K.M. Jr. Implementation and testing of a frozen density matrix - divide and conquer algorithm. J. Phys. Chem., 1999, 103, 1868– 1875. [233] van der Vaart, A.; Merz, K.M. Jr. Divide and conquer interaction energy decomposition. J. Phys. Chem. A, 1999, 103, 3321–3329. [234] Raha, K.; van der Vaart, A.; E. Riley, K.; B. Peters, M.; M. Westerhoff, L.; Kim, H.; Merz Jr., K.M. Pairwise decomposition of residue interaction energies using semiempirical quantum mechanical methods in studies of protein-ligand interaction. J. Am. Chem. Soc., 2005, 127, 6583–6594. [235] Wang, B.; Brothers, E.N.; van der Vaart, A.; Merz Jr., K.M. Fast semiempirical calculations for nuclear magnetic resonance chemical shifts: A divide-and-conquer approach. J. Chem. Phys., 2004, 120, 11392–11400. [236] Wang, B.; Raha, K.; Merz Jr., K.M. Pose scoring by NMR. J. Am. Chem. Soc., 2004, 126, 11430–11431. [237] Wang, B.; Merz, K.M. Jr. A fast QM/MM (quantum mechanical/molecular mechanical) approach to calculate nuclear magnetic resonance chemical shifts for macromolecules. J. Chem. Theory Comput., 2006, 2, 209–215. [238] Gohlke, H.; Kuhn, L. A.; Case, D. A. Change in protein flexibility upon complex formation: Analysis of Ras-Raf using molecular dynamics and a molecular framework approach. Proteins, 2004, 56, 322–327.

298

Bibliography [239] Ahmed, A.; Gohlke, H. Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory. Proteins, 2006, 63, 1038– 1051. [240] Fulle, S.; Gohlke, H. Analyzing the flexibility of RNA structures by constraint counting. Biophys. J., 2008, DOI:10.1529/biophysj.107.113415.

299

Index accept, 63 aexp, 175 alpb, 56 alpha, 104 amoeba_verbose, 84 arad, 57 arange, 175 arnoldi_dimension, 142 atnam, 170 atomn, 47 awt, 175 beeman_integrator, 84 bellymask, 27 bond_umb, 82 ccut, 183 chkvir, 47 chngmask, 39 clambda, 100 cobsl, 182 coeff, 37 comp, 31 conflib_filename, 142 conflib_size, 142 conv, 95 corr, 96 crgmask, 105 criteria, 95 cter, 178 cut, 35 cutcap, 33 cutfd, 64 cutnb, 64 cutres, 63 cwt, 182 dataset, 181 datasetc, 182

300

dbfopt, 63 dbonds_umb, 82 dcut, 181 decompopt, 64 dftb_chg, 94 dftb_maxiter, 94 dftb_telec, 94 dgpt_alpha, 83 dia_shift, 80 diag, 95 diag_routine, 95 dielc, 35 dij, 181 dipmass, 40 dipole_scf_iter_max, 85 dipole_scf_tol, 85 diptau, 40 diptol, 40 dis, 97 disper, 93 dist_gauss, 83 do_debugf, 47 do_vdw_longrange, 85 do_vdw_taper, 85 dobsl, 181 dprob, 62 drms, 27, 141 dt, 28 dumpfrc, 47 dwt, 181 dx0, 27 dynlmb, 105 ee_damped_cut, 85 ee_dsum_cut, 84 eedmeth, 38 eedtbdns, 38 egap_umb, 82

INDEX emap, 81 emix, 175 ene_avg_sampling, 202 energy_window, 142 epsin, 61 epsout, 61 eq_cmd, 154 es_cutoff, 202 evb_dyn, 79 ewald, 92 explored_low_modes, 142 extdiel, 55 fcap, 33 fft, 38 fft_grids_per_ang, 203 fillratio, 62 frameon, 39 freezemol, 181 frequency_eigenvector_recalc, 142 frequency_ligand_rotrans, 142 gbsa, 56 gigj, 181 grnam1, 174 hybridgb, 118 ialtd, 171 iamoeba, 36 iat, 168 iatr, 177 ibelly, 27 icfe, 100 iconstr, 174 icsa, 182 id, 181 id2o, 176 idc, 91 idecomp, 26, 100 ievb, 36, 71 ifntyp, 174 ifqnt, 36 ifsc, 104 ifvari, 171, 172 ig, 30 igb, 36, 54

igr1, 173 ihp, 175 imin, 23 imult, 171 indmeth, 39 ineb, 133 int, 93 intdiel, 55 invwt1, 175 ioutfm, 26 ipimd, 151, 154, 156 ipnlty, 34 ipol, 36 iprot, 177, 179 ips, 38 iqmatoms, 91 ir6, 174 iresid, 171 irest, 24 irstdip, 40 irstyp, 171 iscale, 34 isgend, 29 isgld, 29 isgsta, 29 istrng, 61 itgtmd, 107 itrmax, 96 ivcap, 33 iwrap, 25 ixpk, 174 jfastw, 32 klambda, 100 kmaxqx, 92 ksqmaxq, 92 lbfgs_memory_depth, 141 ligcent_list, 144 ligstart_list, 144 lmod_job_title, 143 lmod_minimize_grms, 143 lmod_relax_grms, 143 lmod_restart_frequency, 143 lmod_step_size_max, 143 lmod_step_size_min, 143

301

INDEX lmod_trajectory_filename, 143 lmod_verbosity, 143 ln, 30 logdvdl, 104 matrix_vector_product_method, 141 maxcyc, 27, 141 maxiter, 40 maxitn, 63 maxsph, 62 mdinfo_flush_interval, 201 mdout_flush_interval, 201 min_xfile, 83 mlimit, 37 mltpro, 179 modvdw, 82 monte_carlo_method, 143 morsify, 81 mpi, 41 mxsub, 34 namr, 177 natr, 177 nbflag, 37 nbias, 79 nbtell, 38 nbuffer, 63 nchain, 154 ncyc, 27 ndip, 181, 182 neglgdel, 47 netfrc, 38 nevb, 79 nfft3, 36 ninc, 171 nme, 178 nmodvdw, 79 nmorse, 79 nmpmc, 178 nmropt, 24 no, 97 no_intermolecular_bonds, 202 noeskp, 34 norest, 105 noshakemask, 32 npbgrid, 63

302

npbverb, 66 npeak, 175 npopt, 64 nprot, 177, 178 nranatm, 47 nrespa, 28 nring, 177 nscm, 28, 156 nsnb, 36 nsnba, 63 nsnbr, 63 nstep1, 171 nstlim, 28, 114 ntave, 25 ntb, 35 ntc, 32 nter, 178 ntf, 35 ntmin, 27, 141 ntp, 31 ntpr, 25 ntr, 27 ntrx, 25 ntt, 29, 151, 154, 156 ntw_evb, 79 ntwe, 26 ntwprt, 26 ntwr, 25 ntwv, 26 ntwx, 25 ntx, 24 ntxo, 25 nuff, 79 num_datasets, 181 number_free_rotrans_modes, 143 number_ligand_rotrans, 143 number_ligands, 143 number_lmod_iterations, 143 number_lmod_moves, 144 numexchg, 114 numwatkeep, 118 nxpk, 174 obs, 177, 179 offset, 56, 65 omega, 175

INDEX optkon, 178 optphi, 178 order, 37 oscale, 176 out_RCdot, 82 param, 154 pbtemp, 61 pencut, 34 phiform, 66 phiout, 65 pme, 92 pres0, 31 printcharges, 96 q, 97 qmcharge, 94 qmcut, 92 qmgb, 93 qmmask, 91 qmqmdx, 94 qmshake, 96 r0, 173 radiopt, 61 random_seed, 144 ranseed, 47 rbornstat, 55 rdt, 56 repcrd, 114 restart_pool_size, 144 restraint, 170 restraintmask, 27 restrt_cmd, 154 rgbmax, 55 rhow_effect, 65 rjcoef, 173 rmsfrc, 47 rotmin_list, 144 rstwt, 169 rtemperature, 144 s11, 181 saltcon, 55 scaldip, 40 scalec, 63 scalm, 34

scee, 36 scfconv, 95 scmask, 104 scnb, 36 sgft, 29 shcut, 177 shrang, 177 skinnb, 38 skmax, 133 skmin, 133 smoothopt, 62 sor_coefficient, 85 space, 62 spin, 94 sprob, 64 str, 177 surften, 56, 65 t, 28 taumet, 176 taup, 31 taurot, 176 tausw, 34 tautp, 30 temp0, 30 temp0les, 30 tempi, 30 tempsg, 29 tgtfitmask, 107 tgtmdfrc, 107 tgtrmsd, 107 tgtrmsmask, 107 theory, 93 tmode, 133 tol, 32, 37 tolpro, 179 total_low_modes, 144 trmin_list, 145 ts_xfile, 83 tsgavg, 29 type, 37 uff, 83 use_axis_opt, 202 use_rmin, 64 use_sav, 65

303

INDEX vdw_cutoff, 202 vdwmeth, 38 verbose, 37 verbosity, 94 vfac, 133 vlimit, 31 vprob, 65 vrand, 30 vv, 133 writepdb, 97 wt, 27, 177, 179 xch_cnst, 80 xch_exp, 80 xch_gauss, 81 xch_type, 79 xdg_xfile, 83 xmin_method, 141 xmin_verbosity, 141 zcap, 33 zerochg, 47 zerodip, 47 zerovdw, 47

304